Simple harmonic motion Questions and Answers

Two particles execute SHM of the same amplitude and frequency along the same straight line If they pass one an other when going in opposite directions each time their displace ment is half their amplitude the phase difference between them is

Charge q is A 8 C Amplitude of motion is NA 10 cm Freqency of oscillation is A 8 B 6 5 C B 20 cm B 10 C 30 cm F 2 kaa 2 2 4 C 5 5 C 9 to 10 D 40 cm kaq xw D 2 f 1 w 271 Equation of SHM displacement from mean position can be expressed as A y 0 1 sin 10 xt y 0 1 sin 10 at 2 C y 0 1 sin 5xt n 2 D 6 5 C D y 0 2 sin 5at 00 phon 2 constant

The potential energy of a particle executing S H M is 25 J when its displacement is half of amplitude The total energy of the particle is 1 250 J 2 180 J 3 100 J 4 25 J

2 A body performs S H M Its kinetic energy K varies with time t as indicated by graph Particle starts from mean position 1 3 KA mm N 2 M KA 0 t Ar t 4 KA t A

12 A simple harmonic oscillator of angular frequency 2 rad s 1 is acted upon by an external force F sint N If the oscillator is at rest in its equilibrium position at t 0 its position at later times is proportional to 1 sint 2 sint 4 3 cost sint 1 1 2 sin 2t 1 2 cc 2 cos 2t sin 2t sin 2t

16 A weightless spring has a force constant k oscillates with frequency f when a mass m is suspended from it The spring is cut into three equal parts and a mass 3 m is suspended from it The frequency of oscillation of one part will now become 1 f 3 f 3 2 2 f 4 3 f

33 A body oscillates with SHM according to the equation x 5 0 m cos 2 rad s t 4 At t 1 5 s its acceleration is 1 139 56 m s 2 139 56 m s 3 69 78 m s 4 60 78 mala til 5 11 0 919 0 A 200x 5X2XX2 A 5 205 31

Equation F bv kx represents equation of a damped oscillations for a particle of 2kg mass where b n2 and k 100 N m then time m after which energy of oscillations will be reduced to half of initial is 4 1 ln2 sec 2 2 sec N S 3 2 n2 sec 4 1 sec

e potential energy of a particle executing SHM along x axis is given by U U U cos ax What he period of oscillation J ma U 2 2 U ma 3 2T a 4 2 aU

A body oscillates with simple harmonic motion of amplitude 4 cm and a frequency of 5 Hz At time t 0 the body is at equilibrium position x 0 and moving in positive direction Write down the equation of simple harmonic motion A particle executes a SHM of period second and amplitude 2 cm Find its acceleration when it is i at the maximum displacement from the mean position and ii at 1 cm from the mean position

The pendulum shown in Figure 1 is pulled to a 5 angle on the left side and released Figure 12 cm Peg 12 cm 1 of 1 wer is shown Your answer 0 82 s was either rounded significant figures than required for this part Part B What is the pendulum s maximum angle on the right side Express your answer in degrees View Available Hint s Grong Submit VAE Provide Feedback Previous Answers PMC Incorrect Try Again 4 attempts remaining Check your geometry You may want to review Hint 1 How to approach the problem

35 II A 28 g rifle bullet traveling 190 m s embeds itself in a 3 1 kg pendulum hanging on a 2 8 m long string which makes the pendulum swing upward in an arc Determine the vertical and horizontal components of the pendulum s maximum displacement

8 A weight is supported by a spring The weight rests 50 cm above a tabletop The weight is pulled down 25 cm and released at time 0 This creates a periodic up and down motion It takes 12 s for the weight to return to the low position cach time Sketch a graph of the height of the weight above the tabletop against time and write an equation to describe the motion high position rest position low position www 75 cm 50 cm 25 cm

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 O 0 2 seconds O2 seconds O 5 seconds 10 seconds

For the next 5 minutes become familiar with the simulation Change various features such as mass length etc Next Click Reset and conduct the following investigation 10 00 00 start pause photogate timer Pendulum 01 02 period 0 000 Start 17 PART 1 will pause play 2 MASS AND NUMBER OF SWINGS Hypothesis As the mass of the pendulum length mass length 2 Show 2nd pendulum 1 50 m mass 2 nono friction ME 1 10 m O real time 1 4 time 1 16 time 1 00 kg 2 10 kg Moon O Earth O Jupiter O Planet X 00 0 Show velocity lots acceleration Show energy of 01 02 Onone photogate timer Mother tools Reset the number of swings this activity keep the length of both pendulums the sam

As the length of the pendulum swings 1 1 5 2 2 5 For this activity the mass should stay the same but the length will change each time Click Reset and conduct the following investigation Length of the Pendulum m 0 5 the number of Use the photogate timer and record the period it takes for each length Remember the period of a pendulum is the time it takes the pendulum to make one full back and forth swing Click reset again Next use the timer by clicking other tools and observe the number of swings the pendulum makes each time you change the length Each time you adjust the length count the number of full swings in a 30 second interval Make sure that the pendulum is released at the same position each time Record the data on the table below Period s Number of swings In 30 seconds

20 Min Test XP Semion Sha app peardeck com t young Chid New Tide CP GM DSMID VC Pada M T 2 1 1 f d v v t Fg mg F mac d v t at v v at r ac v v 2ad 7 4 pts A NASA expedition to an unknown planet has brought a pendulum that has a length of 45 cm If the period is 2 5 s then what is the gravitational acceleration on this planet

3 II An elastic cord is 61 cm long when a weight of 75 N hangs from it but is 85 cm long when a weight of 210 N hangs from it What is the spring constant k of this elastic cord

Which variable will most affect the period of a pendulum Olength amplitude Onone of the above Omad MOLTE PANE TECHNIKER

When a family of four with a total mass of 250 kg step into their 1248 kg car the car s springs compress 2 1 cm a What is the spring constant of the car s springs Fig 11 4 assuming they act as a single spring

Spring 2022 1 30 points You yes you are glowing This is because everything that is at a temperature above absolute zero which is everything gives off electromagnetic radiation light But you re not giving off visible light you re giving off infrared light so we d need to be wearing infrared goggles to see it If your body temperature is 37 C then you re giving off the greatest amount of infrared light at a frequency of 3 2x10 Hz Since your cells are mostly water let s look at one water H O molecule and let s assume that the oxygen atom is mostly staying still and one of the hydrogen atoms is vibrating at this frequency of 3 2x10 3 Hz resulting in this infrared radiation We can model this oscillation as a mass on a spring A hydrogen atom is just a proton and an electron and you can ignore the mass of the electron because it s so small 1 1 6 pts How much time does it take for the hydrogen atom to go through one full oscillation 1 2 8 pts If you re modeling the hydrogen oxygen bond as a spring what is its spring constant 1 3 8 pts Our mass on a spring has both kinetic energy and potential energy For reasons that we won t get into here the total kinetic potential energy on average should be kBT where ka is Boltzmann s constant and T is the temperature What is the amplitude of the oscillation 0 1 4 8 pts What is the hydrogen atom s maximum speed while it is oscillating

8 A radio transmission tower sways in a strong wind so that the top moves back and forth as much as 56 cm with a period of 6 0 s This motion can be modeled using a sine function 7 marks a Sketch a graph of the sideways displacement of the tower d from its normal position as a function of time t for 12 0 s 1 2 3 4 5 6 7 8 9 10 11 12

A spring on Earth has a 0 500 kg mass suspended from one end and the mass is displaced by 0 3 m What will the displacement of the same mass on the same spring be on the Moon where the acceleration due to gravity is one sixth that of Earth Show your work

19 II A mass resting on a horizontal frictionless surface is attached to one end of a spring the other end is fixed to a wall It takes 3 6 J of work to compress the spring by 0 13 m If the spring is compressed and the mass is released from rest it experiences a maximum acceleration of 12 m s Find the value of a the spring constant and b the mass

Why did you measure 10 periods of the pendulum instead of just 1 Would your measurements be improved by measuring 100 periods instead of 10 Why or why not How many periods do you think is the optimal number to measu B T T 0 Word s

What is the earliest time at which the oscillator shown below is stationary E t 1 35 s A B C D t 0 0 s t 0 30 s t 0 45 s t 0 90 s 0 10 m 0 0 10 m Unit s F t 1 80 s w0

Having landed on a newly discovered planet an astronaut sets up a simple pen dulum of length 1 99 m and finds that it makes 592 complete oscillations in 1190 s The amplitude of the oscillations is very small compared to the pendulum s length What is the gravitational the surface of this planet Answer in units of m s acceleration on Answer in units of m s 2

The graph represents the simple harmonic motion of a mass on spring Which arrow indicates the amplitude of the motion Displacement B C A A B C D Time

What is the length in meters of a simple pendulum if it has a period of 4 92 s Assume that the pendulum is on a planet where the acceleration due to gravity is 13 05 m s

A 1 5 meter long pendulum on an unknown planet has a period of 4 seconds What is the acceleration due to gravity on this planet

What is the frequency in Hertz of a simple pendulum on Earth if it has a length of 1 42 m

11 Find the period and frequency of a pendulum on Earth if it has a length of 0 5 meters 12 1865

What is the period in seconds of a simple pendulum on Earth if it has a length of 3 99

What is the mass in kg of an object on a vertical mass spring system with a spring constant of 55 8 N m and a frequency of 1 47 Hz

N P A mass of 2 23 kg is placed on a vertical spring What is the spring constant in N m of a mass spring system with a period of 1 05 s

Find the acceleration due to gravity in m s on a hypothetical planet where a 1 44 m long simple pendulum has a frequency of 0 42 Hz

at is the length of a pendulum on Earth if its period is 5 seconds

What is the period in seconds of a simple pendulum if it has a length of 5 88 m Assume that the pendulum is on a planet where the acceleration due to gravity is 7 85 m s

What is the length in meters of a simple pendulum on Earth if it has a frequency of 0 33 Hz

8 How long would you have to make a pendulum that is to operate on Mars and have a period of 5000 seconds The acceleration due to gravity on Mars is 3 611 m s

The pendulum arm on a clock is to swing back and forth once every 0 5 seconds The bob on the end of the pendulum is 20 grams How long does the pendulum arm need to

What would be the period of an oscillating spring that has a mass of 1 92 kg attached to it if the spring constant has a value of 0 800 N m 4 06 s 9 735

Suppose that a 38 7 kilogram mass is mounted on the end of a horizontal ideal massless spring with stiffness 608 N m Ignore all friction If the mass is initially released from rest when the spring is stretched to an initial displacement of 6 36 centimeters away from its equilibrium position what will be the mass s greatest speed in meters second during the subsequent natural oscillations m s Hint Watch out for unit conversions Your final answer should lie between 0 1 and 0 9 m s

Advanced Physics a When air resistance is ignored does a pendulum clock run faster or slower at higher altitude b Does your answer change if you don t ignore the effects of air resistance

A mass is placed on a spring and oscillates What is the mass if the spring has a spring constant of 500 N m and oscillates with a frequency of 2 Hz

A mass of 7 05 kg is placed on a vertical spring What is the period in seconds of a mass spring system if it has a spring constant of 92 33 N m

10 Find the period and frequency of an oscillating spring with a spring constant of 100 N m and an attached mass of 200 kg

hat is the spring constant of an oscillating spring with a 4 kg mass if it has a riod of 3 seconds

2 A pendulum sways to the left and right according to the model d t 0 8 sin 72 t where d is the displacement in centimeters from the rest position and is the time in seconds Round your answers to the nearest tenth of a unit a Determine the displacement of the pendulum after 6 seconds

You attach a mass to a spring hung from the ceiling pulls the mass 17 cm below its equilibrium position and release it If the amplitude of motion decreases by 12 each second and the mass oscillates 8 times each second find a formula for the distance D the mass is below equilibrium t seconds after you release it D t cm