Oscillations Te...

A simple pendulum has time period $$T _ { 1 }.$$ The point of suspension is now moved upward according to equation $$y = K t ^ { 2 }$$ where $$K = 2.5 \mathrm { m } / \mathrm { s } ^ { 2 }.$$ If new time period is $$T _ { 2 }$$ then ratio will be

The time period of oscillation of a $$SHM$$ is $$\frac { \pi } { 2 } s.$$ Its acceleration at a phase angle $$\frac { \pi } { 3 }\ rad$$  from extreme position is $$2 m s ^ { - 2 }.$$ What is its velocity at a displacement equal to half of its amplitude from mean position? (in $$m s ^ { - 1 }$$)

A particle undergoes SHM. When its displacement is 8 cm, it has speed 3 m/s and a speed 4 m/s at displacement of 6cm. Find time period of oscillation.

If a spring has time $$T$$, and is cut into $$n$$ parts , then the time period of each part will be 

If function $$\sin^{2}(\omega t)$$ represents position of a particle from the origin as function of time, then motion of particle is

A block of mass $$10\,Kg$$ is suspended through two light spring balances as shown in figure.

A particle moves along a straight line such that its displacement(s) at any time(t) is given by $$S=t^3-3t^2+2$$. The velocity of the particle when its acceleration zero is?

The time period of a particle in simple  harmonic motion is equal to the time between consecutive apperance of the particle at a particular point in its motion. This point is 

A particle is executing S.H.M. with amplitude $$'a'$$ and has maximum velocity $$'v'$$. Its speed at displacement $$a/2$$ will be

Spring in vehicles are introduces to: