Exam 14: Oscillations

The figure shows mass m₁ resting on top of mass m₂ which is attached to a spring with spring constant 10 N/m,where m₁ = m₂ = 20 g.The coefficient of static friction between the two masses is 0.6.The masses are oscillating with SMH on a frictionless surface.What is the maximum amplitude of oscillation without m₁ slipping off m₂?

A vertical spring with a spring constant of 4.00 N/m and has a 1.00-kg mass attached to it.The mass is released from rest at a position of 3.00 cm from equilibrium position.If after 100 seconds,the amplitude has decreased to 1.5 cm,what is the damping constant?

A vertical spring is hanging from the ceiling with a mass attached to it.The mass is set to oscillate with SHM by pulling on it.Which of the following would increase the frequency of oscillation?

An object is undergoing simple harmonic motion.The equation of motion of the object is y = Asin( $\omega$ t+ $\delta$ ).The equation for the acceleration as a function of time is

Simple harmonic motion requires that the magnitude of the net restoring force is proportional to the magnitude of which quantity?

Water fills a length of 25 cm of a U tube.Water is slightly displaced and allowed to move freely inside the tube. Assuming the amount of water in the curved section of the U-tube is negligible,what is the period of its motion?

In the small angle approximation,the angle must be measured in

A spring of with a constant k is attached to a mass M.In order to double the frequency of oscillation of this system,I should

The period of a 1.30-m long simple pendulum in an elevator that is 2.52 s.The elevator is accelerating uniformly.What is the acceleration of the elevator?

A 250-g metal cube connected to a light spring of constant 25 N/m oscillates on a horizontal,frictionless surface.The amplitude of its motion is 4 cm.The maximum velocity is

A 5-kg block is attached to a horizontal spring of constant 500 N/m.It is pulled 20 cm from its equilibrium position and released.What is its angular frequency?

A spring is suspended from the ceiling.When a mass of m kg is attached to the spring,it stretches d₁ m.The mass is then pulled down an additional d₂ m and released.Which one of the following statements is true concerning the equation of motion of the mass?

When the displacement of a mass on a spring is one half of the amplitude of its oscillation,what fraction of the total energy is potential energy?

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

A grandfather clock oscillates both on Earth and on the Moon.Where is the period of oscillation the greatest?

What is the total energy of a 15-kg mass attached to a spring oscillating horizontally with an amplitude of 20 cm and an angular frequency of 32 rad/s?

A 2.0-kg mass attached to a spring is displaced 8.0 cm from equilibrium position.It is released and it oscillates with a frequency of 4.0 Hz.What is the speed of the block when it is 6.5 cm from equilibrium? Assume that the surface is frictionless.

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 = 5.0 kg is moving to the left at v_O.The two masses then collide and stick together.If the maximum compression of the spring is 1.2 m,what was the initial velocity of the second mass (v_O)?

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.The driving frequency $\omega$ _d that will produce the largest amplitude response in the mass's oscillation is

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 = 3.0 kg is moving to the left at v_O = 8.0 m/s.The two masses then collide and stick together.What is the maximum compression of the spring?