Physics
Oscillation
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#177 The displacement of an object attached to a spring and executing simple harmonic motion is given by \(x=2 \times 10^{-2} \cos \pi t\) meters. The time at which the maximum speed first occurs is
A) 0.5 s
B) 0.75 s
C) 0.125 s
D) 0.25 s
#178 A particle is executing SHM with a time period of 2 s. When it is at its extreme position, the velocity of the particle is
A) Maximum
B) Half of maximum
C) Zero
D) One fourth of maximum
#179 A simple harmonic oscillator has an amplitude A and time period T. The time required by it to travel from \(x=A\) to \(x=A/2\) is
A) T/6
B) T/4
C) T/3
D) T/2
#180 In simple harmonic motion, the restoring force is always directed
A) Towards the mean position
B) Away from the mean position
C) In the direction of motion
D) Opposite to the direction of motion
#181 The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is
A) 0
B) \(\pi/2\)
C) \(\pi\)
D) 2\(\pi\)
#182 The motion of a simple pendulum is approximately simple harmonic for small amplitudes because
A) The restoring force is proportional to displacement
B) The restoring force is constant
C) The pendulum moves in a circle
D) The potential energy is constant
#183 The acceleration of a particle performing SHM is 12 cm/sec² at a distance of 3 cm from the mean position. Its time period is
A) 2.0 s
B) 3.14 s
C) 0.5 s
D) 1.05 s
#184 A particle is executing SHM along a straight line. Its velocities at distances \(x_1\) and \(x_2\) from the mean position are \(v_1\) and \(v_2\), respectively. Its time period is
A) \(\frac{2 \pi \sqrt{x_2^2 - x_1^2}}{\sqrt{v_1^2 - v_2^2}}\)
B) \(\frac{2 \pi \sqrt{v_1^2 + v_2^2} (x_1 + x_2)}{\sqrt{v_1^2 + v_2^2}}\)
C) \(\frac{2 \pi \sqrt{x_1^2 - x_2^2}}{\sqrt{v_2^2 - v_1^2}}\)
D) \(\frac{2 \pi \sqrt{v_1^2 - v_2^2}}{\sqrt{x_1^2 - x_2^2}}\)
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