On average, a human heart is found to beat 75 times in a minute. Its frequency and period respectively are:

1.  2.25 Hz and 0.8 sec

2.  1.35 Hz and 0.9 sec

3.  1.25 Hz and 0.8 sec

4.  1.25 kHz and 0.8 sec

The time period of the following periodic motions respectively are:

(a) sinωt + cosωt

(b) sinωt + cos2ωt + sin4ωt

1.  $\frac{2\mathrm{\pi }}{\mathrm{\omega }} \mathrm{and} \frac{2\mathrm{\pi }}{3\mathrm{\omega }}$

2.  $\frac{2\mathrm{\pi }}{\mathrm{\omega }} \mathrm{for} \mathrm{both}$

3. $\frac{2\mathrm{\pi }}{3\mathrm{\omega }} \mathrm{for} \mathrm{both}$

4.  $\frac{3\mathrm{\pi }}{\mathrm{\omega }} \mathrm{and} \frac{2\mathrm{\pi }}{\mathrm{\omega }}$

The time period of the following simple harmonic motions respectively are:

(1) sin ωt – cos ωt

(2) sin²ωt

1.  $\frac{2\mathrm{\pi }}{\mathrm{\omega }} \mathrm{and} \frac{\mathrm{\pi }}{\mathrm{\omega }}$

2.  $\frac{2\mathrm{\pi }}{\mathrm{\omega }} \mathrm{and} \frac{\mathrm{\pi }}{2\mathrm{\omega }}$

3.  $\frac{2\mathrm{\pi }}{\mathrm{\omega }} \mathrm{and} \frac{4\mathrm{\pi }}{\mathrm{\omega }}$

4.  $\frac{\mathrm{\pi }}{\mathrm{\omega }} \mathrm{and} \frac{3\mathrm{\pi }}{\mathrm{\omega }}$

A body oscillates with SHM according to the equation (in SI units) x = 5cos [2π t + π/4].

At t = 1.5 s, the displacement and speed of the body respectively are:

1.  $3.535 \mathrm{m} \mathrm{and} 24 \mathrm{m}/\mathrm{s}$

2.  $-3.535 \mathrm{m} \mathrm{and} 24 \mathrm{m}/\mathrm{s}$

3.  $-3.535 \mathrm{m} \mathrm{and} 22 \mathrm{m}/\mathrm{s}$

4.  $3.535 \mathrm{m} \mathrm{and} 22 \mathrm{m}/\mathrm{s}$

What is the length of a simple pendulum, which ticks seconds?
1. \(0.5~\text{m}\)
2. \(1~\text{m}\)
3. \(5~\text{m}\)
4. \(2~\text{m}\)

A 5 kg collar is attached to a spring of spring constant 500 N/m. It slides without friction over a horizontal rod. The collar is displaced from its equilibrium position by 10.0 cm and released. The period of oscillation of the collar is:

1.  $6.3 \sec$

2.  $63 \sec$

3.  $0.63 \sec$

4.  $6 \sec$