A simple pendulum is executing simple harmonic motion with a time period T. If the length of the pendulum is increased by 21%, the increase in the time period is
21%
10%
30%
50%
The potential energy of a long spring when stretched by 2 cm is U. If the spring is stretched by 8 cm the potential energy stored in it is
4U
8U
16 U
U/4
A mass of 2.0 kg is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and released the mass executes a simple harmonic motion. The spring constant is 200 N/m. What should be the minimum amplitude of the motion, so that the mass gets detached from the pan ?(Take g =10m/s2 )
8.0 cm
10.0 cm
Any value less than 12.0 cm
4.0 cm
A point performs simple harmonic oscillation of period T and the equation of motion is given by After the elapse of what fraction of the time period the velocity of the point will be equal to half of its maximum velocity ?
A simple pendulum hangs from the ceiling of a car. If the car accelerates with uniform acceleration, the frequency of the simple pendulum will
increase
decrease
become infinite
remain constant
The displacement x (in metres) of a particle performing S.H.M is related to time t (in second) as :
0.5 Hz
1.0 Hz
1.5 Hz
2.0 Hz
Two simple pendulums having lengths 0.5 m and 2.0 m are displaced linearly a little at the same time. They will be in the same phase when shorter pendulum completes oscillations equal to
2
5
3
1
A body is vibrating in S.H.M. with an amplitude of 0.06 m and frequency of 15 Hz. The maximum velocity and acceleration of the body are
5.65 m/s, 5.32 x 102 m/s2
6.82 m/s, 7.62 x 102 m/s2
8.91 m/s, 8.21 x 102 m/s2
9.82 m/s, 9.03 x 102 m/s2
In a simple harmonic motion, if the displacement is half of the amplitude, then which part of total energy will be kinetic energy ?
1/3
3/4
2/3
1/4
A particle is performing simple harmonic motion along x axis with amplitude 4 cm and time period 1.2 sec. The minimum time taken by the particle to move from x = + 2 cm to x = + 4 cm and back again is
0.4 s
0.3 s
0.2 s
0.6 s