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 |
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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 |
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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 |
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The metallic bob of a simple pendulum has the relative density ρ. The time period of this pendulum is T. If the metallic bob is immersed in water, then the new time period is given by

(1) Tρ-1ρ                 

(2)     Tρρ-1

(3) Tρ-1ρ               

(4) Tρρ-1

Subtopic:  Simple Harmonic Motion |
 66%
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The period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination θ, is given by -

1.   2πLgcosθ               

2.  2πLgsinθ

3.  2πLg                      

4. 2πLgtanθ

Subtopic:  Simple Harmonic Motion |
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One end of a long metallic wire of length L is tied to the ceiling. The other end is tied to massless spring of spring constant K. A mass m hangs freely from the free end of the spring. The area of cross-section and Young's modulus of the wire is A and Y respectively. If the mass is slightly pulled down and released, it will oscillate with a time period T equal to -

(1)    2πmK                   

(2)     2πYA+KLmYAK1/2

(3)    2πmYAKL               

(4)      2πmLYA

Subtopic:  Combination of Springs |
 72%
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On a smooth inclined plane, a body of mass M is attached between two springs. The other ends of the springs are fixed to firm supports. If each spring has force constant K, the period of oscillation of the body (assuming the springs as massless) is

(a) 2πM2K1/2           (b) 2π2MK1/2

(c) 2πMg sinθ2K           (d) 2π2MgK1/2

                

Subtopic:  Combination of Springs |
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