Oscillations

A mass is suspended separately by two different springs in successive order, then time periods are t1 and t2 respectively. If it is connected by both springs as shown in figure then time period is t0, the correct relation is [figure]

1. t02 = t12 + t22
2. t0-2 = t1-2 + t2-2
3. t0-1 = t1-1 + t2-1
4. t0 = t1 + t2

The total energy of particle performing SHM depends on

1. k, a, m
2. k, a
3. k, a, x
4. k, x

Two masses MA and MB are hung from two strings of length lA and lB respectively. They are executing SHM with frequency relation fA = 2fB, then relation

1. lA = lB4, does not depend on mass
2. lA = 4lB, does not depend on mass
3. lA = 2lB and MA = 2MB
4. lA = lB2 and MA = MB2

The bob of simple pendulum having length l, is displaced from mean position to an angular position with respect to vertical. If it is released, then velocity of bob at equilibrium position

1. 2gl(1 - )
2. 2gl(1 + )
3. 2gl
4. 2gl

The equations of two waves acting in perpendicular directions are given as x = a ( t + ) and y = a ( t + ), where = + 2, the resultant wave represents

1. a parabola
2. a circle
3. an ellipse
4. a straight line