Exam 14: Oscillations

A 3.0-kg mass is attached to a spring with a spring constant of 7.0 N/m and set into simple harmonic motion with an amplitude of 5.0 cm.When the mass has 36% of its maximum kinetic energy,how far away is it from its equilibrium position?

A particle in simple harmonic motion has an angular frequency of 24 rad/s.Its maximum acceleration is 400 m/s².What is its maximum velocity?

A particle in simple harmonic motion has an angular frequency of 24 rad/s.Its maximum velocity is 25 m/s.What is the amplitude of its oscillation?

Two objects oscillate on springs in simple harmonic motion.Object 1 has mass M₁,amplitude A₁,and a spring with a spring constant k₁.Object 2 has M₂ = 5 M₁,A₂ = 2 A₁,and k₂ = 1.5 k₁.How do the total energies of these two systems compare?

A mass m₁ = 7.0 kg is at rest on a frictionless horizontal surface and connected to a wall by an ideal spring with a spring constant of k = 50 N/m as shown in the figure.A second mass m₂ = 7.0 kg is moving to the left at v_O = 8.0 m/s.The two masses then collide elastically.What is the maximum compression of the spring?

A mass of 1.35 kg rests on a frictionless floor and is attached to a wall with a 25.0-cm long spring with spring constant 1250 N/m.The mass is pulled back away from the wall to stretch the spring to a length of 34.5 cm.The mass is then released.The speed of the block when the spring returns to its original (unstretched)length is

A mass M = 2.54 kg is attached to a wall with a spring with spring constant k = 375 N/m.The mass slides on a frictionless floor.The spring and mass are immersed in a fluid with damping coefficient 8.25 kg/s.An external sinusoidal horizontal force F(t)= F_dcos( $\omega$ _dt),where F_d = 75.4 N,is applied to the mass,causing the mass to oscillate back and forth.You may neglect the mass of the spring.What is the largest amplitude response in the mass's oscillation this driving force can produce?

A vertical spring with a spring constant of 4.00 N/m,has a 1.00-kg mass attached to it,and moves in a medium with a damping constant 0.025 kg/s.The mass is released from rest at a position of 3.0 cm from equilibrium position.How long will it take for the amplitude to decrease to 1.0 cm?

A 2.0-kg mass is connected to a 5.0-kg mass by a massless rod 32 cm long,as shown in the figure.A hole is then drilled in the rod 11 cm away from the 2.0-kg mass and the rod and masses are free to rotate about this pivot point P.What is the period of rotational oscillations for the masses if they are displaced slightly from equilibrium?

An oscillator has a Q factor of 150.In one period its energy is decreased by

A mass m₁ = 7.0 kg is at rest on a frictionless horizontal surface and connected to a wall by an ideal spring with a spring constant of k = 50 N/m as shown in the figure.A second mass m₂ = 7.0 kg is moving to the left at v_O.The two masses then collide elastically.If the maximum compression of the spring is 1.2 m,what was the initial velocity of the second mass (v_O)?

Consider the two pendulums shown in the figure.The one on the left has a 2.0-kg mass attached to a 3.0-m long string,while the one on the right has two 1.0-kg masses that are separated by a 2.0-m long string and then hung from another 2.0-m string.Which pendulum will have a shorter period?

A mass of 0.404 kg is attached to a spring with spring constant 204.9 N/m.Its oscillation is damped with a damping constant of b = 15.7 kg/s.What is the angular oscillation frequency of this damped oscillation? (in rad/s)

Imagine you are an astronaut who has landed on another planet and you want to determine the free fall acceleration on that planet.In one of the experiments you decided to conduct,you use a pendulum 0.50 m long and find that the period of oscillation for this pendulum is 2.15 s.What is the acceleration of gravity on that planet?

A 7.2-kg mass oscillates on a horizontal spring.The position of the object is given by the relation (all units in MKS).The system is then submerged into a vat of oil with a damping constant of 1.42 kg/s.How long will it take before the amplitude of oscillations becomes 0.314 m?

The position of a particle moving along x-axis is given by x = 0.05 sin (15(rad/s)t + 0.5 rad)m.Its acceleration at t = 0.5 sec is

An object connected to a spring oscillates with simple harmonic motion.The amplitude of the motion is A,the equilibrium position is x = 0,the angular frequency is .What is the speed of the object when it is located at x = A/2? Ignore friction and air resistance.

A 2.0-kg mass is connected to a 5.0-kg mass by a massless rod 32 cm long,as shown in the figure.A hole is then drilled in the rod 11 cm away from the 2.0-kg mass and the rod and masses are free to rotate about this pivot point P.What is the angular frequency of rotational oscillations for the masses if they are displaced slightly from equilibrium?

A mass that can oscillate without friction on a horizontal surface is attached to a horizontal spring and is pulled to the right and is released from rest.The period of the oscillation is 5.60 s.The speed of the mass is m/s at t = 0.50 s.What is the amplitude of the oscillation?

A vertical spring with a spring constant of 4.00 N/m,has a 1.00-kg mass attached to it,and moves in a medium with a damping constant 0.025 kg/s.The mass is released from rest at a position of 3.00 cm from equilibrium position.What is the amplitude of the oscillation after 20 seconds have elapsed?