Q- A harmonic force F0 sin(ωt) is applied to mass m1 which in turn is coupled to springs of spring constants k1, k2 and k3. Let x1 and x2 be the deviations from equilibrium for m1 and m2, respectively. The blocks moves on a horizontal frictionless table.
(a) Write the equations of motion for …
Q- A simple fatigue testing machine has a moving base that is 15kg and is constrained to only move vertically. The base is supported by a rubber block with a spring constant, k = 18 kN/m and a viscous damping constant of c = 200N.s/m. A rotating mass which is part of the base creates a harmonic forc…
Q- A 1.5 kg piston supported on a helical spring vibrates freely with a natural frequency of 3Hz. When oscillating within an oil filled cylinder the frequency of free oscillation is reduced to 2.90Hz.
(a) Find the stiffness of the helical spring.
(b) Find the damping ratio when in the oil filled …
Q- A particle executes linear harmonic motion about the point x = 0. At t = 0, it has a displacement x = 0.37 cm and zero velocity. The frequency of oscillation is 0.25 Hz. Determine
(a) The period (b) the angular frequency (c) the amplitude (d) the displacement at time t (e) the velocity at time t…
Q- A block is suspended by a vertical spring of constant 1800 N/m and makes 5.5 oscillations per second.
(a) Find the mass of the block.
(b) What is elongations in the spring if the block is at rest in equilibrium?
(c) If the block is pulled down by 2.5 cm from equilibrium position and released, …
Q- A particle M executes simple harmonic motion along x axis. The reference particle for this SHM moves on a circular path of radius R = 40 cm with a constant speed of 80 cm/s.
(a) Find the angular frequency, frequency and the time period for this SHM.
(b) If at t = 0, the reference particle makes…
Q- A bungee jumper whose mass is 95 kg, has just completed his first bungee jump and is now bouncing up and down at the end of the cord. His oscillations have initial amplitude of 7 m and a period of 4.0 s.
(a) What is the spring constant of the bungee cord?
(b) What is the jumper's maximum speed …
Q- A small block of mass 80 g is oscillating on a spring. The equation of motion for its position x as a function of time is given by
x(t) = (5.0 cm) cos (10t + π/4)
(a) what is the amplitude of the oscillation?
(b) What is the period of oscillation?
(c) What is the…
Q- Astronauts in space cannot weigh themselves by standing on a bathroom scale. Instead, they determine their mass by oscillating on a large spring. Suppose an astronaut attaches one end of a large spring to her belt and the other end to a hook on the wall of the space capsule. A fellow astronaut th…
Q. A 170 g mass attached to a horizontal spring oscillates at a frequency of 2.0 Hz. At t = 0 s, the mass is at x = 5.0 cm and has vx = -28 cm/s. Determine the following.
(a) The period (b) The angular frequency (c) The amplitude (d) The phase constant (e) The maximum speed (f) The maximum acc…
A block attached to a spring with unknown spring constant oscillates with a period of 3.0 s.
(a) What is the period if the mass is doubled?
(b) What is the period if the mass is halved?
(c) What is the period if the amplitude is doubled?
(d) What is the period if the spring constant is doubled?
…Q- A block with mass M attached to a horizontal spring with force constant k is moving with simple harmonic motion having an amplitude A . At the instant when the block passes through its equilibrium position, a lump of putty with mass m is dropped vertically onto the block from a very small height …
A uniform cylinder of mass m is rotated through a small angle from the equilibrium position and released. The stiffness of the spring fixed to the cylinder is k. The radius of the cylinder is r. The spring is connected at a distance a from the center of the cylinder. The cylinder rolls without slipp…
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