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

 

Subtopic:  Simple Harmonic Motion |
 79%
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Hints

Which of the following functions of time represent/s periodic motion? [ω is any positive constant]

(a) sinωt + cosωt

(b) sinωt + cos2ωt + sin4ωt

(c) eωt

(d) log(ωt)

(e) sin2ωt

1.  (a)

2.  (a), (b) and (d)

3.  (a), (b) and (e)

4.  All

 

Subtopic:  Types of Motion |
 66%
From NCERT
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The time period of the following periodic motions respectively are:

(a) sinωt + cosωt

(b) sinωt + cos2ωt + sin4ωt

1.  2πω and 2π3ω

2.  2πω for both

3. 2π3ω for both

4.  3πω and 2πω

 

Subtopic:  Simple Harmonic Motion |
 67%
From NCERT
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The time period of the following simple harmonic motions respectively are:

(1) sin ωt – cos ωt

(2) sin2ωt

1.  2πω and πω

2.  2πω and π2ω

3.  2πω and 4πω

4.  πω and 3πω

 

Subtopic:  Simple Harmonic Motion |
 72%
From NCERT
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The figure given below depicts two circular motions. The radius of the circle, the period of revolution, the initial position, and the sense of revolution are indicated in the figures.  Equations of the x-projection of the radius vector of the rotating particle P in each case are, respectively:


 
1. \(\mathrm{x}(\mathrm{t})=\mathrm{A} \cos \left(\frac{2 \pi}{4} \mathrm{t}+\frac{\pi}{4}\right)\text{ and }\mathrm{x}(\mathrm{t})=\mathrm{B} \cos \left(\frac{\pi}{15} \mathrm{t}-\frac{\pi}{2}\right)\)
2. \(\mathrm{x}(\mathrm{t})=\mathrm{A} \cos \left(\frac{2 \pi}{4} \mathrm{t}+\frac{\pi}{4}\right)\text{ and }\mathrm{x}(\mathrm{t})=\mathrm{B} \sin \left(\frac{\pi}{15} \mathrm{t}-\frac{\pi}{2}\right)\)
3. \(\mathrm{x}(\mathrm{t})=\mathrm{A} \cos \left(\frac{2 \pi}{4} \mathrm{t}+\frac{\pi}{4}\right)\text{ and }\mathrm{x}(\mathrm{t})=\mathrm{B} \cos \left(\frac{\pi}{15} \mathrm{t}-\frac{\pi}{4}\right)\)
4. \(\mathrm{x}(\mathrm{t})=\mathrm{A} \sin \left(\frac{2 \pi}{4} \mathrm{t}+\frac{\pi}{4}\right)\text{ and }\mathrm{x}(\mathrm{t})=\mathrm{B} \cos \left(\frac{\pi}{15} \mathrm{t}-\frac{\pi}{2}\right)\)
Subtopic:  Linear SHM |
From NCERT
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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 m and 24 m/s

2.  -3.535 m and 24 m/s

3.  -3.535 m and 22 m/s

4.  3.535 m and 22 m/s

Subtopic:  Simple Harmonic Motion |
 50%
From NCERT
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Two identical springs of spring constant \(k\) are attached to a block of mass \(m\) and to fixed supports as shown in the figure. When the mass is displaced from its equilibrium position on either side, it executes a simple harmonic motion. The period of oscillations is:

   

1. \(2 \pi \sqrt{\frac{\mathrm{m}}{4 \mathrm{k}}}\)
2. \(2 \pi \sqrt{\frac{2\mathrm{m}}{ \mathrm{k}}}\)
3. \(2 \pi \sqrt{\frac{\mathrm{m}}{2 \mathrm{k}}}\)
4. \(2 \pi \sqrt{\frac{\mathrm{m}}{ \mathrm{k}}}\)

Subtopic:  Combination of Springs |
 84%
From NCERT
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A block whose mass is \(1\) kg is fastened to a spring. The spring has a spring constant of  50 N m-1. The block is pulled to a distance \(x = 10\) cm from its equilibrium position at \(x = 0\) on a frictionless surface from rest at \(t=0.\) The kinetic energy of the block when it is \(5\) cm away from the mean position is:
1. 1.9 J
2. 0.29 J
3. 0.19 J
4. 2.9 J

Subtopic:  Energy of SHM |
 67%
From NCERT
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What is the length of a simple pendulum, which ticks seconds?

1.  0.5 m

2.  1 m

3.  5 m

4.  2 m

 

Subtopic:  Simple Harmonic Motion |
 72%
From NCERT
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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

 

Subtopic:  Simple Harmonic Motion |
 81%
From NCERT
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