Obtain an expression for the period of oscillations of a mass attached to end of a spring and undergoing shm. Obtain expression for K.E. and P.E. at any position during shm.

Write down the expression for the period of oscillation of a mass attached to (i) a horizontal spring and (ii) a vertical spring.

Derive an expression for the P.E. and K.E. of a body executing shm.

Derive an experession for the period of oscillation of a mass attached to a spring executing simple harmonic motion. Given that the period of oscillation depends on the mass m and the force constant k, where k is the force required to stretch the spring by unit length?

Is oscillation of a mass suspended by a spring simple harmonic ? give expression for its time period also.

At what displacement K.E. and P.E. are equal, for a body executing shm.

Obtain an expression for intensity of electric field in end on position, i.e., axial position of an electric dipole.

One end of an ideal spring is fixed to a wall at origin O and axis of spring is parallel to x-axis. A block of mass m = 1kg is attached to free end of the spring and it is performing SHM. Equation of position of the block in co-ordinate system shown in figure is x = 10 + 3 sin (10t) . Here, t is in second and x in cm . Another block of mass M = 3kg , moving towards the origin with velocity 30 cm//s collides with the block performing SHM at t = 0 and gets stuck to it. Calculate (a) new amplitude of oscillations, (b) neweqution for position of the combined body, ( c) loss of energy during collision. Neglect friction.

One end of an ideal spring is fixed to a wall at origin O and axis of spring is parallel to x-axis. A block of mass m = 1kg is attached to free end of the spring and it is performing SHM. Equation of position of the block in co-ordinate system shown in figure is x = 10 + 3 sin (10t) . Here, t is in second and x in cm . Another block of mass M = 3kg , moving towards the origin with velocity 30 cm//s collides with the block performing SHM at t = 0 and gets stuck to it. Calculate (a) new amplitude of oscillations, (b) neweqution for position of the combined body, ( c) loss of energy during collision. Neglect friction.

A block of mass m is tied to one end of a spring which passes over a smooth fixed pulley A and under a light smooth movable pulley B . The other end of the string is attached to the lower end of a spring of spring constant K_2 . Find the period of small oscillation of mass m about its equilibrium position (in second). (Take m=pi^2kg , K_2k=4K_1 , K_1=17(N)/(m). )

There are two ideal springs of force constants K_1 and K_2 respectively. When both springs are relaxed the separation between free ends is L. Now the particle of mass m attached to free end of left spring is displaced by distance 2L towards left and then released. assuming the surface to be frictionless. ((K_(1))/(K_(2))=4/3) . (Neglect size of the block) Suppose mass m hits the right spring and sticks to it. The extension in left spring when mass ‘m’ is in equilibrium position during its motion is :