# Which one of the following equations of motion represents simple harmonic motion? (where $$k,k_0,k_1~\text{and}~a$$ are all positive.) 1. Acceleration $$=-k_0x+k_1x^2$$ 2. Acceleration $$=-k(x+a)$$ 3. Acceleration $$=k(x+a)$$ 4. Acceleration $$=kx$$

Subtopic:  Simple Harmonic Motion |
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NEET - 2009
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Two simple harmonic motions of angular frequency $$100~\text{rad s}^{-1}$$ and $$1000~\text{rad s}^{-1}$$ have the same displacement amplitude. The ratio of their maximum acceleration will be:
1. $$1:10$$
2. $$1:10^{2}$$
3. $$1:10^{3}$$
4. $$1:10^{4}$$

Subtopic:  Linear SHM |
86%
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NEET - 2008
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An SHM has an amplitude $$a$$ and a time period $$T.$$ The maximum velocity will be:
1. $${4a \over T}$$
2. $${2a \over T}$$
3. $${2 \pi \over T}$$
4. $${2a \pi \over T}$$
Subtopic:  Simple Harmonic Motion |
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A particle is executing simple harmonic motion with frequency $$f$$. The frequency at which its kinetic energy changes into potential energy, will be:
1. $$\frac{f}{2}$$
2. $$f$$
3. $$2f$$
4. $$4f$$
Subtopic:  Energy of SHM |
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In a simple pendulum, the period of oscillation $$T$$ is related to length of the pendulum $$L$$ as:
1. $$\frac{L}{T}= \text{constant}$$
2. $$\frac{L^2}{T}= \text{constant}$$
3. $$\frac{L}{T^2}= \text{constant}$$
4. $$\frac{L^2}{T^2}= \text{constant}$$
Subtopic:  Angular SHM |
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A pendulum has time period $$T$$. If it is taken on to another planet having acceleration due to gravity half and mass $$9$$ times that of the earth, then its time period on the other planet will be:
 1 $$\sqrt{T}$$ 2 $$T$$ 3 $${T}^{1 / 3}$$ 4 $$\sqrt{2} {T}$$
Subtopic:  Angular SHM |
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A simple pendulum hanging from the ceiling of a stationary lift has a time period $$T_1$$. When the lift moves downward with constant velocity, then the time period becomes $$T_2$$. It can be concluded that:
 1 $$T_2 ~\text{is infinity}$$ 2 $$T_2>T_1$$ 3 $$T_2 Subtopic: Angular SHM | 61% From NCERT To view explanation, please take trial in the course. NEET 2025 - Target Batch Hints To view explanation, please take trial in the course. NEET 2025 - Target Batch If the length of a pendulum is made \(9$$ times and mass of the bob is made $$4$$ times, then the value of time period will become:
1. $$3T$$
2. $$\dfrac{3}{2}T$$
3. $$4T$$
4. $$2T$$

Subtopic:  Angular SHM |
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A body performs simple harmonic motion about $$x=0$$ with an amplitude a and a time period $$T$$. The speed of the body at $$x= \frac{a}{2}$$ will be:
1. $$\frac{\pi a\sqrt{3}}{2T}$$
2. $$\frac{\pi a}{T}$$
3. $$\frac{3\pi^2 a}{T}$$
4. $$\frac{\pi a\sqrt{3}}{T}$$
Subtopic:  Linear SHM |
77%
From NCERT
NEET - 2009
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The displacement of a particle along the $$x\text-$$axis is given by $$x= a\sin^2\omega t$$. The motion of the particle corresponds to:
 1 simple harmonic motion of frequency $$\frac{\omega}{\pi}$$. 2 simple harmonic motion of frequency $$\frac{3\omega}{2\pi}$$. 3 non-simple harmonic motion. 4 simple harmonic motion of frequency $$\frac{\omega}{2\pi}$$.
Subtopic:  Simple Harmonic Motion |
From NCERT
NEET - 2010
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