Simple harmonic motion Questions and Answers

The graph represents the simple harmonic motion of a pendulum Which arrow indicates the period of the motion Displacement A C D B C D Time

6 A heavy 7 kg mass on a weak 12 N m spring oscillates with an amplitude o 23 cm 6a 1 1 point graded At what frequency in Hz does the mass oscillate 0 208 0 208

WA AA AA c 27 Describe the motion shown by the diagrams above write the general equation of me use sin or cos A or A Draw the horizontal spring mass system and show the initial position and initial veloc

A 3 kilogram mass hangs from a spring with a constant of 4 newtons per meter The mass is set into motion by giving it a downward velocity of 3 meters per second Damping in newtons equal to five times the velocity in meters per second acts on the mass during its motion At time t 6 seconds it is struck upwards with a hammer imparting a unit impulse force Set up the initial value problem to compute the displacement of the mass as a function of time

Speed V of particle moving in a straight line is given by V 144 16 x all quantities are in SI unit x is distance from fixed point then Acceleration is not uniform Particle is performing SHM 75 O Time period of SHM is 4 Amplitude of SHM is 3 unit

A block of mass 3 kg is subjected to force F 18x at t 0 particle is at x 6 and is at rest then find Location of mean position

In a simple harmonic motion with force F kx and amplitude A oscillating about a mean position at x 0 Average KE from x 0 to x A is equal to 0 KA Average KE for one complete oscillation during one time period is equal to KA Average PE from x 0 to x A is equal to KA 6 KA Average PE for one complete oscillation during one time period is equal to KA

Simple pendulum In the figure a 0 24 kg ball is suspended from a very light string 9 79 m long and is pulled slightly to the left As the ball swings without friction through the lowest part of its motion it encounters an ideal massless spring attached to the wall The spring pushes against the ball and eventually the ball is returned to its original starting position Find the time for one complete cycle of this motion if the spring constant of the spring is 21 N m Assume that once the pendulum ball hits the spring there is no effect due to the vertical movement of the ball 9 79 m 0 24 kg 1 000 wall

If masses of 100 grams and 400 grams are hanging from two identical springs and the 100 gram mass oscillates with a period of 7 0s then the 400 gram mass will oscillate with period of a 7 2 s b 7 4 s Oc 7s d 7 x 2 s

The position of a simple harmonic oscillator is given by x t 0 500 m cos 1 20t where t is in seconds Match the quantities in the right column to their correct values in the second column Angular frequency w frequency f Amplitude of oscillation A Period T 1 0 500 m 2 1 20 rad s 3 rad s 4 0 191 Hz 5 5 24 S

A 2 kg object attached to a horizontal spring oscillates with an amplitude A 6 cm and frequency f 1 8 Hz The maximum speed of the object is 21 6 cm s 33 9 cm s 10 8 cm s 67 9 cm s None of these answers is correct

4 What is the mass suspended from a spring of 100 N m making 10 complete cycles in 35 seconds

2 What is the period of a mass spring oscillation system with a spring constant of 355 N m and mass of 10 kg

A 4 3 m long simple pendulum oscillates with a period of 4 4 s on the surface of an unknown planet What is the surface gravity of the planet

3 What is the spring constant of a mass spring oscillating system making 25 complete oscillations in 30 seconds when a mass of 0 6 kg is suspended from the spring

6 A simple pendulum with a length of 3 m oscillates on the Moon s surface where acceleration due to gravity is 2 0 m s What is the period of oscillations

A large motor in a factory causes the floor to vibrate up and down at a of 10 4 Hz The frequency amplitude of the floor s motion near the motor is about 3 3 mm Estimate the maximum acceleration of the floor near the motor

A spider of mass 0 44 g waits in its web of negligible mass A slight movement causes the web to vibrate with a frequency of about 13 Hz At what frequency would you expect the web to vibrate if an insect of mass 0 4 g were trapped in addition to the spider

A geologist uses a simple pendulum that has a length of 38 85 cm and a frequency of 0 8116 Hz at a particular location on the Earth What is the acceleration due to gravity at this location

A spider of mass 0 29 g waits in its web of negligible mass A slight movement causes the web to vibrate with a frequency of about 16 Hz At what frequency would you expect the web to vibrate if an insect of mass 0 22 g were trapped in addition to the spider

A geologist uses a simple pendulum that has a length of 37 58 cm and a frequency of 0 5457 Hz at a particular location on the Earth What is the acceleration due to gravity at this location

A geologist uses a simple pendulum that has a length of 44 54 cm and a frequency of 0 3956 Hz at a particular location on the Earth What is the acceleration due to gravity at this location

A geologist uses a simple pendulum that has a length of 39 93 cm and a frequency of 0 5395 Hz at a particular location on the Earth What is the acceleration due to gravity at this location

A spider of mass 0 36 g waits in its web of negligible mass Fig 11 6 A slight movement causes the web to vibrate with a frequency of about 17 Hz a Estimate the value of the spring stiffness constant k for the web

A spider of mass 0 37 g waits in its web of negligible mass Fig 11 6 A slight movement causes the web to vibrate with a frequency of about 21 Hz b At what frequency would you expect the web to vibrate if an insect of mass 0 33 g were trapped in addition to the spider

3 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

7 The following position time function shows the motion of an oscillating mass on a spring Vertical Position Speed Net Force Acceleration 8 Kinetic Energy 12 16 Identify the following positions on the graph by using the times on the x axis 20 X Maximum 20 38 Minimum Time s

v t w Asin 2nt T WA 0 50 0 50 0 50 T 4 1 00 T Z 1 50 3T 4 2 00 T 2 50 5T 4 3 00 31 Z 3 50 7T 4 1 s Fig 3b 1 Indicate where the displacement is maximum by marking the graph with a symbol of your choice 2 Indicate where the displacement is minimum by placing a star on the graph 4 ZT N

displacement of block m 1 0 5 0 0 5 1 10 m 5 0 time s 5 1 Label the points where velocity is maximum by circling them Indicate if the velocity is positive or negative 2 Label the points where velocity is zero by marking them with any 10

1 The following position time function shows the motion of an oscillating mass on a spring Vertical Position 10 Speed Net Force Acceleration Kinetic Energy 12 Potential Energy 16 Identify the following positions on the graph by using the times on the x axis Maximum 20 24 X 28 32 36 Minimum Time s

What is the elastic potential energy stored in a spring whose spring constant is 160 N m when it is compressed 8 0 cm 0 51 J

A block attached to a spring with a force constant of 85 N m is undergoing simple harmonic motion on a horizontal frictionless surface The period of vibration of this block is 0 55 s a What is the mass of the block b What is the frequency of the vibration

and Energy Draw the three energy diagrams for this pendulum Support Maximum Point String Bob Equilibrium Point Energy Pie Charts Maximum Point OC

The following image shows a mass on an oscillating spring The mass is moving from position A to B and then to C Once at C it returns in the other direction m www Tw Speed Net Force Acceleration Kinetic Energy Potential Energy Maximum Minimum

05 09 HC A message in a bottle is floating on top of the ocean in a periodic manner The time between periods of maximum heights is 24 seconds and the average height of the bottle is 8 feet The bottle moves in a manner such that the distance from the highest and lowest point is 4 feet A cosine function can model the movement of the message in a bottle in relation to the height Part A Determine the amplitude and period of the function that could model the height of the message in a bottle as a function of time t 5 points Part B Assuming that at t 0 the message in a bottle is at its average height and moves upwards after what is the equation of the function that could represent the situation 5 points Part C Based on the graph of the function after how many seconds will it reach its lowest height 5 points

An ball is connected to a string as shown The ball moves downward from position A with a speed vo Traveling on a circular path the ball stops at position B What enables the ball to reach point B which is above point A Ignore friction and air resistance

b How fast will the mass be traveling when it returns to the equilibrium position E f J 202 17 5 pts A m 0 60 kg mass attached to a spring with spring constant k 90 N m is undergoing simple harmonic motion on a frictionless surface When the mass is x 0 1 m from its equilibrium position its speed is momentarily zero a What is the frequency of the mass s oscillations toooooooo C 2 0 60 90 K 12 r X A 22 x 0 6 5130199321 Arequency 2 83 HIL X A

A tennis coach paces back and forth along the sideline 10 times in 2 minutes The frequency of her pacing is Hz

2T T 2 T T 2 26 A simple pendulum having a bob of mass M has a period T If you double M but change nothing else what would be the new period

1 A wave can best be described as O a a transfer of potential energy from a medium Ob a motion of a light source O c a vibration in space and time O d a negative displacement of motion 2 An example of a mechanical wave is O an X ray O a Microwave O Visible Light an Ocean Wave

19 The speed of sound in ice water and steam is shown What best explains the speed of sound in different states of matter Medium Ice Water Steam Temperature C 0 25 100 Speed of Sound m s 3200 m s 1500 m s 346 m s 2p O Sound travels fastest in ice because energy is easier to transfer when the molecules are close together Sound travels slowest in steam because the sound has to move around the gas molecules that are far apart Sound travels fastest in ice because the temperature of solids is always greater so the heat transfers the sound energy O Sound travels slowest in steam because the pressure is so great the sound cannot travel though the steam particles

9 The graph represents the simple harmonic motion of a pendulum Which arrow indicates the Period of the motion Displacement O A OB O C O D A B C D Time

The graph represents the simple harmonic motion of a pendul Which arrow indicates the Amplitude of the motion Displacement O A B O C O D A B C D Time

5 Two waves traveling in opposite directions on a rope meet and undergo complete destructive interference Which of the following best describes the waves a moment AFTER the waves meet and coincide O a The waves no longer exist O b The waves continue unchanged O c The waves reflect and travel backward Od A single wave continues along the rope 6 Standing waves are produced by periodic waves of a any frequency amplitude and wavelength traveling in the same direction b any frequency amplitude and wavelength traveling in opposite directions Oc the same frequency amplitude and wavelength traveling in the same direction Od the same frequency amplitude and wavelength traveling in opposite directions

A mass Mis attached to a spring with spring constant k When this system is set in motion with amplitude A it has a period T What is the period if the amplitude of the motion is increased to 3A T 2 T 3T 9T T 3

A mass of 0 150 kg is attached to a spring with a force constant of 3 58 N m and undergoes simple harmonic oscillations What is the period of the oscillations 1 14 s 2 57 s 0 263 s

21 A 2 0 kg box is trave stationary 6 0 kg bo N m as shown in th frequency of the os 5 0 m s

A mass attached to a very light spring executes simple harmonic motion If you want to double its total energy you should double the force constant of the spring while changing nothing else double the mass while changing nothing else double both the mass and amplitude of vibration double both the amplitude and force constant double the amplitude of vibration while changing nothing else

4 Given the equation for simple harmonic motion d 8 sint where d is in feet and t is in seconds a Find the maximum displacement with correct units b Find the period of the motion with correct units c Find the frequency of the motion with correct units d Find the least positive value of t with correct units for which d 0 e Sketch the graph of the equation for ONE period Include labels for any intercepts maximum or minimum values

5 Suppose a 1 4 kg mass is attached to a spring with spring constant k 4 N m Suppose the spring is in a medium that offers a damping force equal to the velocity If the mass is released from rest from a point 1 2 meter above equilibrium find the equation of motion