Exam 14: Oscillations

A simple pendulum has a period of 3.65 s on the surface of the Earth.If this pendulum were placed on the surface of the Moon,where the gravitational acceleration is 1.62 m/s²,what would its period be?

A 7.2-kg mass oscillates on a horizontal spring.The position of the object is given by the relation (all units in MKS).What is the spring constant of the spring?

An object undergoing simple harmonic motion in the x-direction has a period of 2.0 seconds,an amplitude of 5 cm and begins its oscillation at t = 0 at its maximum value of x.What equation could describe its motion?

A mass on a spring oscillates with a period T.If we increase the mass by a factor 8 and at the same time double the spring constant of the spring,then the length of the new oscillation period of the spring will be

The motion of a block- spring system is described by x = A sin ( $\omega$ t).Find $\omega$ knowing that the potential energy equals the kinetic energy for the first time at t = 2.00 s.

When Bobby swings on a swing,his period of oscillation is 2.5 s.When Geraldine,who is half Bobby's mass,rides the exact same swing,what is the ratio of her period of oscillation to his?

A pendulum is composed of a mass of 2.00 kg suspended from the ceiling by a string.The pendulum makes 1000 complete oscillations in an hour.What is the length of the string in m?

What is the frequency of a 1.30-m long simple pendulum in an elevator that is moving upward with a uniform acceleration of 1.20 m/s²?

A dense 1.00-kg mass is attached to a 1.35-m long massless rod that is free to swing from the top.The entire system is placed in a fluid with a small drag force b = 0.120 Ns/m = 0.120 kg/s and the rod is released from an initial displacement angle of 6.00 ^$\circ$ from vertical.What is the time it takes for the oscillation amplitude to reduce to 3.00 ^$\circ$ ? You may assume that the damping is small.Also note that since the amplitude of oscillation is small and all the mass of the pendulum is at the end of the rod,the motion of the mass can be treated as strictly linear and we can use the substitution: R $\theta$ (t)= x(t),where R = 1.35 m is the length of the pendulum rod.

The energy of an oscillator decreases by 6.0% in one period.What is its Q factor?

A 20-kg mass is placed on a horizontal frictionless surface and then connected by two springs with spring constants k₁ = 5.0 N/m and k₂ = 3.0 N/m to walls as shown in the figure.What is the period of oscillations for the 20-kg mass if it is displaced slightly to one side?

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 kinetic energy?

What is the period of oscillation for a 0.50-kg block which slides on a horizontal,frictionless plane,and is attached to a spring having spring constant 25 N/m?

How long must a pendulum on the Moon be if it is to have a period of 2.00 seconds? (Acceleration of gravity on the moon is 1.62 m/s².)

A cube of wood (side length 3.2 cm,mass 24 g)floats on the surface of a pond.A frog jumps off of it and it begins to oscillate in simple harmonic motion with a frequency of 5.0 Hz.What is the effective value of the spring constant of water?

A simple harmonic oscillator consists of an object on a spring,with the whole of the apparatus in a vat of fluid.If the damping constant is exactly one tenth that required for critical damping,what is the ratio of the damped period to the oscillator's period if set in motion outside the vat of fluid?

A seconds pendulum is a pendulum whose period is precisely two seconds;one second for a swing in one direction and one second for the return swing.The length of a seconds pendulum in Tokyo,Japan is 0.9927 m and that in Cambridge,England is 0.9942 m.The ratio of the acceleration due to gravity at the two places,g_T /g_L is

What is the period of a 1.30-m long simple pendulum in an elevator that is moving downward with a uniform acceleration of 1.20 m/s²?

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

A pendulum on a distant planet oscillates 20 times in 10.0 seconds.The length of the pendulum is 25.0 cm.What is the acceleration due to gravity on this planet? Ignore friction and air resistance.