Simple harmonic motion Questions and Answers

Calibri Brass 69 7 g Cork 2 8 g Lead 86 5 g 11 What is the period for each pendulum 12 points Mass Period seconds Wood 5 3 g Steel 65 9 g T Aluminum 23 6 g P Conclusions Part II A H

When a mass of 530 g is attached to a vertical spring and lowered to its equilibrium position it is found that the spring extends 16 0 cm If the mass is now displaced from its equilibrium position what is the period in seconds of the resulting oscillations Use g 9 80 m s 2 Your Answer

What is the total energy of a 315 g mass that is attached to a horizontal spring with a force constant of 383 0 N m and oscillates along a frictionless horizontal surface with an amplitude of 15 0 cm Your Answer

A system consists of a mass vibrating on the end of a spring The total mechanical energy of this system O is always equal to the square of the amplitude is constant regardless of the displacement of the mass from the equilibrium position varies as a sine or cosine function is constant only when the mass is at maximum displacement is a maximum when the mass is at its equilibrium position only

The force constant for a simple harmonic motion is k and the amplitude of the motion is A The maximum value of the potential energy of a mass moscillating with simple harmonic motion is 2 mik OKA KA KA 2kA

A wave has a period 2 00 s an amplitude 20 0 cm and a wavelength 3 00 m What is the speed of the wave 340 m s 0 100 cm s 1 50 m s 0 667 m s 10 0 cm s

The position of a mass that is oscillating on a spring is given by x 0 360 m cos 19 3 s t What is the period in s of this motion Your Answer

The velocity of an object vibrating along the x axis obeys the equation v 0 800 m s sin 46 0 rad s t What is the magnitude of the maximum acceleration in m s2 of the vibrating object Your Answer

A 0 400 kg block on a horizontal frictionless surface is attached to an ideal massless spring whose spring constant is 270 0 The block is pulled from its equilibrium position at x 0 000 m to a displacement x 0 080 m and is released from rest The block then executes simple harmonic motion along the horizontal x axis What is the potential energy of the system in J when the block is at x 0 040 m from the equilibrium Give your answer in Sl units Your Answer

Which one of the pendulums oscillates v 10 cm 100 g Pendulum A 12 cm 200 g C 15 cm 100 g D 12 50 g

The figure below shows the position versus time graph of an ob harmonic motion Determine the period and amplitude of oscilla x cm 8 T 4 AA 5 10 15 0 4 81 O Period 0 1 s Amplitude 8 cm Period 5 s Amplitude 16 cm Period 10 s Amplitude 8 cm t s 20

An object has a position given by x (t) = At where A = 0.677 m/s4. What is the velocity of the object at time t = 1.36 s? Express your answer in m/s to 3 significant figures.

Professor Graves tries to entertain his cats by tying a plastic mouse to the end of a horizontal spring. He tests the setup, pulling the 0.25 kg mouse 25 cm to the right from equilibrium, then letting go. During this test he notes that over 10 seconds, 18 oscillations were completed. Figuring this would be sufficiently fast, he lets in the cats. What is the position and velocity of the mouse when the cats catch it one second later?

Say you just woke up in the morning, and while going to take a shower you realized you had a physics test to take. Because of the joy overwhelming you to take such a test, you break out into song. You modulate your voice until you hear your voice resonate in the shower, producing standing sound waves. You can treat the shower stall as a 2.5 m high "pipe", closed at each end by the ceiling and floor. You can treat the air as room temperature, such that a wave traveling across it would travel at 343 m/s. a. What is the fundamental frequency to produce a standing sound wave? b. What wavelength, wavenumber, and period correspond to this frequency?

If a simple harmonic oscillator has got a displacement of 0.04 m and acceleration equal to 3.06 m/s² at any time, what is the angular frequency of the oscillator in radian/sec? Round your answer to 2 decimal places.

For the spring/mass system with an external force of the form Fext = sin(bt), what needs to be the case to see the exact phenomenon of beats? No damping, and a natural frequency in yc of exactly b. No damping, and a natural frequency in yc close to b. Light damping, and a natural frequency in yc of exactly b. Light damping, and a natural frequency in yc close to b.

A particle moves along a line so that, at time t, its position is s(t) = 5 sin(6), t>0. a. What is the first time t that the particle changes direction? b. For what values of t does the particle change direction? [1] c. What is the particle's maximum velocity? [2] [5]

The displacement of an object is described by this equation, where x is in meters and t is in seconds: x = (0.42 m) cos(9.6t) What is the frequency (Hz) of the oscillating object? Round your answer to 2 decimal places.

The springs of a 1500 kg car compress 5mm when its 68 kg driver gets into the driver's seat. If the car goes over a bump, what will be the frequency of vibrations? A) 2.0 Hz B2.25 Hz C) 1.5 Hz D) 1.75 Hz

The length of a simple pendulum is 0.56 meters, the pendulum bob has a mass of 481 g, and it is released at an angle of 12 degrees to the vertical. With what frequency (in Hz) does it vibrate? Round your answer to 2 decimal places.

A weight suspended from a spring is seen to bob up and down over a distance of 39 cm twice each second. What is its frequency? Answer in units of Hz.

15. The diagram represents wavelengths of different colors of visible light that pass by in a specific time period. Which color of light has the greatest frequency? Red Yellow Blue Violet a. Red b. Yellow c. Blue d. Violet

Investigation 1.2 For each variable, determine whether or not your measurements are the same or different within the uncertainty. In the space below, for each variable discuss, based on your measurements, whether it affects the period of a pendulum and why or why not. Mass: Displacement: Length:

A mass hanging from a spring undergoes vertical simple harmonic motion. Where in the motion is the magnitude of the net force equal to zero? At the highest point in the oscillation. At the lowest point in the oscillation. At the point half-way between the highest point and the lowest point. At the point where the spring is unstretched. At any point the net force is not zero. Where in the motion is the velocity equal to zero? Check all that apply. At the highest point in the oscillation. At the point half-way between the highest point and the lowest point. At the point where the spring is unstretched. At the lowest point in the oscillation.

Find the magnitude of average velocity of a particle executing SHM starting from positive extreme till it moves a distance 3A/2 if A is the amplitude and T is time period 9A/2T 6A/T 2A/3T A/27

Energy in SHM: A 1.8-kg mass attached to an ideal massless spring with a spring constant of 24.0 N/m oscillates on a horizontal, frictionless track. At time t = 0.00 s, the mass is released from rest at x = 10.0 cm. (That is, the spring is stretched by 10.0 cm.) (a) Find the frequency of the oscillations. (b) Determine the maximum speed of the mass. At what point in the motion does the maximum speed occur? (c) What is the maximum acceleration of the mass? At what point in the motion does the maximum acceleration occur? (d) Determine the total energy of the oscillating system. (e) Express the displacement x as a function of time t.

A particle executes SHM between x = -A and x = + A. The time taken for it to go from x = 0 to A/2 is T₁ and to go from to A/2 to A is T₂. The time period of oscillation is 4T, then T₁+T₂=T T=3T₁ T= 2T₂ T₁=2T₂

A mass of 0.100 kg connected to a spring with a spring constant 5.00 N/m. (a) Calculate the period and the frequency of the motion. (b) When an unknown mass is connected, the frequency was 1.25 Hz. What is the mass? (c) You take this spring-mass system to the moon. Will the period change? Explain.

Position of a particle is given by x = A sin(wt + θ) where x is in meter and w, are constants. Find the velocity of the particle at time t. A. Aw cos(wt + θ) B. - Aw cos(wt + θ) C. Aw² cos(wt + θ) D. Aw² cos(wt + θ)

Mechano, the evil robot ccat, has captured the mouse, Jerry (m=0.600 kg), and is about to launch him out of a window using his robotic sling shot. The slingshot has two elastic bands that hold the pouch, which is wrapped around Jerry. Treat each of the bands like a Hooke's Law spring, with a spring constant of k=1850 N/m. The rest length of each "spring" is Lo= 5.00 x 10-2 m. Answer the two questions below, using three sig figs. Part A-Just befor the launch, the "springs" have a length of Ly = 0.120 m. How much elastic potential energy. Ug. is stored in each "spring?" Part B - What is Jerry's speed, vy, when he leaves the slingshot?

The pendulum is a device that measures time. Calculate the length of the mathematical pendulum that shows time 1 second on Earth. Explain what can cause this clock run slower or faster (three factors).

A child with poor table manners is sliding his dinner plate back and forth in SHM with an amplitude of 10 cm on a horizontal surface. At a point 6 cm away from equilibrium, the speed of the plate is 40 cm/s. What is the period?

A steel wire of length L connects a hook on the ceiling to a bowling ball, With the steel wire kept taut, the bowling ball is lifted to a height h above the floor, and then released. The bowling ball swings back and forth in the motion of a pendulum. After the bowling ball is released, what is the maximum height above the floor that it reaches? Assume that friction does not affect its motion. Oh/2 1.33h h OL Oh

A 24 kg mass is undergoing simple harmonic motion with an amplitude of 25 cm. If the force constant of the spring is 50 N/m: a. Calculate the total energy of the mass spring system b. Calculate the maximum kinetic energy of the system c. Calculate the acceleration experienced by the mass at 5 cm from the equilibrium point

A geologist suspends a 0.30-kg stone on an ideal spring. In equilibrium the stone stretches the spring 2.0 cm downward stone is then pulled an additional distance of 1.0 cm down and released from rest. (a) Write do ne equation for the vertical position y of the stone as a function of time t, using the cosine function. Take the origin at the equilibrium point of the stone, with the positive y direction upward. (b) How fast is the stone moving at a time equal to 1/3 of its period of motion?

Read the section in your Physics textbook or verified resource that discusses wave phenomena, simple harmonic motion and the relevant terminology (i.e., wavelength, frequency, period, and wave speed). Complete the problems on this sheet and submit it before proceeding with the experiment. 1. A wave of frequency 400.0 Hz has a wavelength of 23 cm. a) What is the period of the wave in seconds? b) What is the period of the wave in ms (milliseconds)? c) What is the wave speed in m/s (meters per second)? I 2. An oscilloscope is set-up to display the above sinusoidal wave as a function of time. If the horizontal axis is calibrated at 1 millisecond/cm, what will be the spacing in centimeters between successive maxima on the screen?

If x, v and a denote the displacement, the velocity and the accelerated of a particle executing simple harmonic motion of time. period T, then, which of the following does not change with time? A. aT/4πV B.aT/V C.a²T² + 4π²v² D.aT/X

A compact car has a mass of 1300 kg. When empty, the car bounces up and down on its springs 2.0 times per second. What is the car's oscillation frequency while carrying four 79 kg passengers?

A guitar string with a linear density of 2.00 g/m is stretched between supports that are 60 cm apart. The string is observed to form a standing wave with three antinodes when driven at a frequency of 420 Hz. What are (a) the frequency of the fifth harmonic of this string and (b) the tension in the string?

A block attached to a horizontal spring is pulled back a certain distance from equilibrium, then released from rest at t = 0 s. If the frequency of the block is 0.80 Hz, what is the earliest time after the block is released that its kinetic energy is exac one-half of its potential energy? Express your answer with the appropriate units.

(a) If you increase the length of a pendulum by a factor of 3, how does the new period T compare to the old period 7? (b) If you decrease the length of the pendulum by 5%, how does the new period TN compare to the old period 7?

When a jumbo egg was dropped from 5 meters onto a 1-inch foam surface, the egg was fractured. According to the egg drop experiment, how much is the change in momentum of the egg? 49.5 kg m/s 123.75 kg m/s 9.9 kg m/s 0.79 kg m/s

An object that completes 100 vibrations in 5 seconds has a period of Select one: a. 0.5 seconds b. none of these c. 1 second d. 2 seconds

A boat moves up and down on a lake as a wave passes by. If the boat oscillates 10 times in 2 seconds, what is the period of the wave? 0.2 seconds 2 seconds 5 seconds 10 second

A block is connected to the end of a spring and bobs up and down over a total distance of 30 cm. It bobs up and down twice every second. The block's frequency is _______Hz. Its period is _____seconds. Its amplitude is ______cm.

A ball is attached to a vertical spring with a spring constant of 6.0 N/m. It is held at the equilibrium position of the spring and then released. It falls 0.40 m and then bounces back up again. Calculate the mass of the ball.

A toy airplane ejects its 8.4 g pilot using a spring with a spring constant of 5.2*10² N/m. The spring is initially compressed 5.2 cm. (a) Calculate the elastic potential energy of the compressed spring. (b) Calculate the speed of the pilot as it ejects upward from the airplane. (c) Determine the maximum height that the pilot will reach.

Part (a) refers to the figure below. Block 1 has a mass m₁ = 0.2 kg and is travelling to the right with an initial speed v₁,i = 2 m/sec. Block 2 is initially at rest, it has a mass m₂ = 0.3 kg, and it is attached to a spring with a spring constant k = 8 N/m. Block 1 then collides with Block 2 and the two blocks stick together after the collision. After the collision, both blocks move to the right and both blocks come to rest after they compress the spring by a distance x. What is x ?

Part (a) refers to the figure below. A block of mass m = 0.1 kg is going down and inclined plane with an initial speed v₁. The inclined plane makes an angle θ= 30° with the horizontal and the inclined plane has a kinetic friction coefficient μk = 0.7. After travelling a distance L = 0.8 m, the block encounters. a spring with a spring constant k = 20 N/m. The block comes to rest after compressing the spring an amount = 0.3 m. What is v₁, the initial speed of the block?

Part (b) refers to the figure below. Block 1 has a mass m₁ = 0.2 kg and is travelling to the right with an initial speed v₁,i = 2 m/sec. Block 2 is initially at rest, it has a mass m₂ = 0.3 kg, and it is attached to a spring with a spring constant k = 8 N/m. Block 1 then collides with Block 2. The collision between Block 1 and Block 2 is a elastic collision. After the collision, block 2 moves to the right and block 2 comes to rest after it compresses the spring by a distance x. What is x?