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Ten questions, one verdict per topic

Answer all ten without looking anything up. The result tells you, topic by topic, which lessons you may skip and which you should read.

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Ten questions. The result tells you which lessons you may skip.

1

Two particles oscillate with the same amplitude and period. One is at its positive extreme while the other passes through the mean position. The phase difference between them is

2

Two SHMs have the same amplitude. The period of the first is \(2\,\text{s}\) and that of the second is \(1\,\text{s}\). The greatest speed of the second is

3

Two SHMs of the same frequency along one line have amplitudes \(3\,\text{cm}\) and \(4\,\text{cm}\) and a phase difference of \(\pi/2\). The amplitude of the resultant motion is

4

Two SHMs of the same frequency along one line, of amplitudes \(5\,\text{cm}\) and \(3\,\text{cm}\), are in opposite phase. The resultant amplitude is

5

A particle moves with \(x = A\sin\omega t\) and \(y = A\cos\omega t\) at the same time. Its path is

6

Two perpendicular SHMs have frequencies in the ratio \(1 : 2\) and start together at the mean position. The path is

7

The amplitude of a damped oscillator halves in \(6\,\text{s}\). Its energy halves in

8

A block on a spring is released from an extreme. It returns to the mean position in the least possible time without crossing it when the damping is

9

A block of natural frequency \(2\,\text{Hz}\) is driven by a periodic force of frequency \(5\,\text{Hz}\). In the steady state it oscillates at

10

The damping of a driven oscillator is reduced. Its resonance peak becomes