In a simple harmonic oscillation, the acceleration against displacement for one complete oscillation will be

A simple pendulum has a time period T₁. When its point of suspension is moved vertically upwards according as y = k t², where y is vertical distance covered and k = 1 ms⁻², its time period becomes T₂. Then, \(\frac { { T }_{ 1 }^{ 2 } }{ { T }_{ 2 }^{ 2 } } \) is (g = 10 m s⁻²).

A hollow sphere is filled with water. It is hung by a long thread. As the water flows out of a hole at the bottom, the period of oscillation will

When a damped harmonic oscillator completes 100 oscillations, its amplitude is reduced to \(\frac{1}{3}\) of its initial value. What will be its amplitude when it completes 200 oscillations?

A mass of 3 kg is attached at the end of a spring moves with simple harmonic motion on a horizontal frictionless table with time period 2π and with amplitude of 2m, then the maximum fore exerted on the spring is

The x-t graph of a particle undergoing simple harmonic motion is shown. The acceleration of the particle at t =\(\frac{4}{3}\) is ______________.

The simple harmonic motions are respresented by the equation. y₁ = 0.1 sin (100πt + π/3) & Y₂= 0.1 cos π the phase difference of the velocity of particle is _________________.

When the maximum k.E of a simple pendulum is k, then what is its displacement in terms of amplitude a when its K.E. is k/2 ____________.

A body of mass 1 kg is executing SHM given by, x = 4 Cos\(\left( 100t+\frac { \pi }{ 2 } \right) \)cm. Whatis the velocity?

A small body of mass 50 g is undergoing SHM of amplitude 100 cm and period 0.2 s. What is the maximum value of the force acting on the body?

A mass m moves with a speed v on a horizontal smooth surface and collides with a nearly massless spring whose spring constant is k. If the mass stops after collision, compute the maximum compression of the spring.

Define frequency of simple harmonic motion.

What is meant by free oscillation?

A piece of wood of mass m is floating erect in a liquid whose density is ρ. If it is slightly pressed down and released, then executes simple harmonic motion. Show that its time period of oscillation is \(T=2 \pi \sqrt{\frac{m}{A g \rho}}\)

Why the amplitude of the vibrating pendulum should be small?

Write down the kinetic energy and total energy expressions in terms of linear momentum, For one-dimensional case.

State five characteristics of SHM.

Every simple harmonic motion is periodic motion but every periodic motion need not be simple harmonic motion. Do you agree? Give example.

In forced oscillation of a particle, the amplitude is maximum for a frequency \({ \omega }\), of the force, while the energy is maximum for a frequency \({ \omega }_{ 2 }\) of the force, what is relation between \({ \omega }_{ 1 }\) and \({ \omega }_{ 2 }\)?

A particle executes SHM with a time period of 16 s. At time t = 2 s, the particle crosses the mean position while at t = 4 s, its velocity is 4 ms^-1, Find its amplitude of motion.

Calculate the amplitude, angular frequency, frequency, time period and initial phase for the simple harmonic oscillation given below
a. y = 0.3 sin (40\(\pi\)t + 1.1)
b. y = 2 cos (\(\pi\)t)
c. y = 3 sin (2\(\pi\)t − 1.5)

Write short notes on the oscillations of liquid column in U-tube.

Explain briefly about oscillations.