A particle executes SHM given by the equation $x = 4 sin (2 \pi t +\pi/4)$, what will be the velocity of the particle at t = (1/8)th sec; ;

A spring-mass system oscillation in a car. if the car accelerates on a horizontal road, the frequency of oscillation will ;

The period of small oscillations is

A particle executes simple harmonic oscillation

with an amplitude a. The period of oscillation is

T. The minimum time taken by the particle to

travel half of the amplitude from the

equilibrium position is:

A point mass $m=20kg$, is suspended by a massless spring of constant $2000 N/m$. The point mass is released when elongation in the spring is $15cm$. The equation of displacement of particle as function of time is: (Take $g=10 m/s^2$)