What is the force equation of a SHM?

A simple pendulum is transferred from earth to the surface of moon. How will its time period be affected?

The piston in the cylinder head of a locomotive has a stroke (twice the amplitude) of 1.0 m. If the piston executes simple harmonic motion with an angular frequency of 200 rad/min, then what is its maximum speed?

Define the restoring force and it characterstic in case of an oscillating body.

Every SHM is periodic motion, but every periodic motion need not to be a simple harmonic motion. Do you agree? Give an example to justify your statement.

The maximum acceleration of a simple harmonic oscillator is a₀ and the maximum velocity is v₀ . What is the displacement amplitude?

A mass attached to a spring free to oscillate, with angular velocity \(\omega \) in a horizontal plane without friction or damping. It is pulled to a distance x₀ and pushed towards the centre with a velocity v₀ at time t = 0. Determine the amplitude of the resulting oscillations in terms of the parameters \(\omega \),x₀ and v₀.

The displacement of two particles executing simple harmonic motion are represented by equations, y = 4 sin (10t +θ) and y₂ = 5 cos 10t. What is the phase difference between the velocities of these particles?

What is the frequency of a second pendulum in an elevator moving up with an acceleration of \(\frac{g}{2}?\) 

The vertical motion of a huge piston in machine is simple harmonic with a frequency of 0.50 s^-1. A block of 10 kg is placed on the piston. What is the maximum amplitude of the piston's SHM for the block and the piston to remain together?

A particle is executing SHM of amplitude A. At what displacement from the mean position is the energy half kinetic and half potential?

A block whose mass is 1 kg is fastened to a spring. The spring has a spring constant of 50 N m^–1. The block is pulled to a distance x = 10 cm from its equilibrium position at x = 0 on a frictionless surface from rest at t = 0. Calculate the kinetic, potential and total energies of the block when it is 5 cm away from the mean position.

What is the length of a simple pendulum, which ticks seconds ?

Plot the corresponding reference circle for each of the following simple harmonic motions. Indicate the initial (t = 0) position of the particle, the radius of the circle, and the angular speed of the rotating particle. For simplicity, the sense of rotation may be fixed to be anti-clockwise in even) case: (x is in cm and t is in s)
(a) x = - 2 sin (3t + \(\pi\)/3)
(b) x = cos (\(\pi\)/6 - t)
(c) x = 3 sin (2\(\pi\)t + \(\pi\)/4)
(d) x = 2 cos \(\pi\)t,

An air chamber of volume V has a neck area of cross section a into which a ball of mass m just fits and can move up and down without any friction (Fig.). Show that when the ball is pressed down a little and released, it executes SHM. Obtain an expression for the time period of oscillations assuming pressure-volume variations of air to be isothermal.

A block is resting on a piston which is moving vertically with a simple harmonic motion of period 1 sec. At what amplitude of motion will the block and the piston seperate? What is the maximum velocity of the piston at this amplitude?

A uniform spring whose unstretched length is I has a force constant k. The spring is cut into two pieces of unstretched lengths. l₁and l₂, where l₁= nl₂ and n is an integer. What are the corresponding force constants k₁ and k₂ in terms of n and k?