# A particle is executing simple harmonic motion with frequency f. The frequency at which its kinetic energy changes into potential energy, will be: 1.   f/2          2.  f 3.   2 f         4.  4 f

Subtopic:  Energy of SHM |
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There is a body having mass m and performing S.H.M. with amplitude a. There is a restoring force ,$F=-Kx$ where x is the displacement. The total energy of body depends upon -

(1)   K, x

(2)  K, a

(3)   K, a, x

(4)  K, a, v

Subtopic:  Energy of SHM |
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The potential energy of a simple harmonic oscillator when the particle is half way to its end point is (where E is the total energy)

(1)    $\frac{1}{8}E$

(2)        $\frac{1}{4}E$

(3)    $\frac{1}{2}E$

(4)        $\frac{2}{3}E$

Subtopic:  Energy of SHM |
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A body executes simple harmonic motion. The potential energy (P.E.), the kinetic energy (K.E.) and total energy (T.E.) are measured as a function of displacement x. Which of the following statements is true ?

(1)  P.E. is maximum when x = 0

(2)  K.E. is maximum when x = 0

(3)  T.E. is zero when x = 0

(4)  K.E. is maximum when x is maximum

Subtopic:  Energy of SHM |
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­­A man measures the period of a simple pendulum inside a stationary lift and finds it to be T sec. If the lift accelerates upwards with an acceleration $\mathrm{g}}{4}$ , then the period of the pendulum will be

(1) T

(2) $\frac{\mathrm{T}}{4}$

(3) $\frac{2\mathrm{T}}{\sqrt{5}}$

(4) $2\mathrm{T}\sqrt{5}$

Subtopic:  Angular SHM |
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The total energy of a particle, executing simple harmonic motion is

(1)

(2)

(3)   Independent of x

(4)

Subtopic:  Energy of SHM |
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The bob of a pendulum of length l is pulled aside from its equilibrium position through an angle $\theta$ and then released. The bob will then pass through its equilibrium position with a speed v, where v equals

(1) $\sqrt{2\mathrm{gl}\left(1-\mathrm{sin\theta }\right)}$

(2) $\sqrt{2\mathrm{gl}\left(1+\mathrm{cos\theta }\right)}$

(3) $\sqrt{2\mathrm{gl}\left(1-\mathrm{cos\theta }\right)}$

(4) $\sqrt{2\mathrm{gl}\left(1+\mathrm{sin\theta }\right)}$

Subtopic:  Angular SHM |
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A body is executing Simple Harmonic Motion. At a displacement x its potential energy is ${E}_{1}$ and at a displacement y its potential energy is ${E}_{2}$. The potential energy E at displacement $\left(x+y\right)$ is

(1)  $E=\sqrt{{E}_{1}}+\sqrt{{E}_{2}}$

(2)  $\sqrt{E}=\sqrt{{E}_{1}}+\sqrt{{E}_{2}}$

(3)   $E={E}_{1}+{E}_{2}$

(4)  None of these.

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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The equation of motion of a particle is $\frac{{d}^{2}y}{d{t}^{2}}+Ky=0$ where K is positive constant. The time period of the motion is given by

(1) $\frac{2\mathrm{\pi }}{K}$

(2) $2\mathrm{\pi K}$

(3) $\frac{2\mathrm{\pi }}{\sqrt{K}}$

(4)  $2\pi \sqrt{K}$

Subtopic:  Simple Harmonic Motion |
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