The displacement of a damped harmonic oscillator is given by `x(t)=e^(-0.1t)cos(10pit+phi)`. Here t is in seconds
The time taken for its amplitude of vibration to drop to half of its initial is close to :

The displacement of a simple harmonic oscillator is given by x = 4 cos (2pit+pi//4)m . Then velocity of the oscillator at t = 2 s is

The position of a simple harmonic oscillator is given by x(t) = (0.50) cos ((pi)/(3)t) , where t is measured in seconds. What is the maximum velocity of this oscillator?

The displacement of a simple harmonic oscillator is, x = 5 sin (pit//3) m . Then its velocity at t = 1 s, is

Equation of motion for a particle performing damped harmonic oscillation is given as x=e^(-1t) cos(10pit+phi) . The time when amplitude will half of the initial is :

The equation of a simple harmonic motion is given by x =6 sin 10 t + 8 cos 10 t , where x is in cm, and t is in seconds. Find the resultant amplitude.

For the damped oscillator shown in Fig, the mass of the block is 200 g, k = 80 N m^(-1) and the damping constant b is 40 gs^(-1) Calculate (a) The period of oscillation (b) Time taken for its amplitude of vibrations to drop to half of its initial values (c) The time for the mechanical energy to drop to half initial values

The equation of displacement of a harmonic oscillator is x = 3sin omega t +4 cos omega t amplitude is

For the damped oscillator shown in previous Figure, the mass m of the block is 400 g, k=45 Nm^(-1) and the damping constant b is 80 g s^(-1) . Calculate . (a) The period of osciallation , (b) Time taken for its amplitude of vibrations to drop to half of its initial value and (c ) The time taken for its mechanical energy to drop to half its initial value.

The displacement equation of an oscillator is given by x = 5 sin (2pit+0.5pi)m . Then its time period and initial displacement are

In damped oscillatory motion a block of mass 20kg is suspended to a spring of force constant 90N//m in a medium and damping constant is 40g//s . Find (a) time period of oscillation (b) time taken for amplitude of oscillation to drop to half of its intial value (c) time taken for its mechanical energy to drop to half of its initial value.