The time period of a simple pendulum of length L as measured in an elevator descending with acceleration g3 is

(1) 2π3Lg

(2) π3Lg

(3) 2π3L2g

(4) 2π2L3g

Subtopic:  Simple Harmonic Motion |
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If a body is released into a tunnel dug across the diameter of earth, it executes simple harmonic motion with time period:
1. \(T = 2\pi \sqrt{\frac{R_e}{g}}\)
2. \(T = 2\pi \sqrt{\frac{2R_e}{g}}\)
3. \(T = 2\pi \sqrt{\frac{R_e}{2g}}\)
4. \(T = 2~\text{s}\)
Subtopic:  Simple Harmonic Motion |
 69%
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If the displacement equation of a particle be represented by y=AsinPt+ Bcos Pt , the particle executes

(1)         A uniform circular motion

(2)         A uniform elliptical motion

(3)         A S.H.M.

(4)         A rectilinear motion

Subtopic:  Simple Harmonic Motion |
 82%
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A particle with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force Fsinωt . If the amplitude of the particle is maximum for ω=ω1  and the energy of the particle is maximum for ω=ω2, then (where ω0 is natural frequency of oscillation of particle)

1. ω1=ω0 and ω2ω0

2. ω1=ω0 and ω2=ω0

3. ω1ω0 and ω2=ω0

4. ω1ω0 and ω2ω0

Subtopic:  Forced Oscillations (OLD NCERT) |
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The displacement of a particle varies according to the relation x = 4(cosπt + sinπt). The amplitude of the particle is

(1)   8           

(2)  – 4

(3)   4          

(4)   42

Subtopic:  Simple Harmonic Motion |
 76%
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A S.H.M. is represented by x=52sin 2πt+cos 2πt. The amplitude of the S.H.M. is

(1)   10 cm         

(2)  20 cm

(3)   52 cm     

(4)  50 cm

Subtopic:  Simple Harmonic Motion |
 76%
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 Amplitude of a wave is represented by

A=ca+b-c

Then resonance will occur when

(1)     b=-c/2              

(2)         b = 0 and a c

(3)     b=-a/2              

(4)         None of these

Subtopic:  Damped Oscillations (OLD NCERT) |
 72%
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The displacement of a particle varies with time as x=12sin wt-16 sin3 wt (in cm). If its motion is S.H.M., then its maximum acceleration is -

(a) 12ω2      

(b) 36ω2

(c) 144ω2       

(d)  192ω2

Subtopic:  Simple Harmonic Motion |
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A particle of mass m is executing oscillations about the origin on the x-axis. Its potential energy is Ux=kx3 , where k is a positive constant. If the amplitude of oscillation is a, then its time period T is -

(1)   Proportional to  1a 

(2)         Independent of a

(3)   Proportional to a   

(4)         Proportional to  a3/2

Subtopic:  Simple Harmonic Motion |
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A cylindrical piston of mass M slides smoothly inside a long cylinder closed at one end, enclosing a certain mass of gas. The cylinder is kept with its axis horizontal. If the piston is disturbed from its equilibrium position, it oscillates simple harmonically. The period of oscillation will be

 

(1) T=2πMhPA

(2) T=2πMAPh

(3) T=2πMPAh

(4) T=2πMPhA

Subtopic:  Simple Harmonic Motion |
 57%
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