Question Bank for JEE Main & Advanced Physics Simple Harmonic Motion Superposition of S H M and Resonance

1)

The S.H.M. of a particle is given by the equation\[y=3\sin \omega \,t+4\cos \omega \,t\]. The amplitude is [MP PET 1993]

A)

7

B)

1

C)

5

D)

12

View Solution

2)

If the displacement equation of a particle be represented by \[y=A\sin PT+B\cos PT\], the particle executes [MP PET 1986]

A)

A uniform circular motion

B)

A uniform elliptical motion

C)

A S.H.M.

D)

A rectilinear motion

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3)

The motion of a particle varies with time according to the relation \[y=a(\sin \omega \,t+\cos \omega \,t)\], then

A)

The motion is oscillatory but not S.H.M.

B)

The motion is S.H.M. with amplitude a

C)

The motion is S.H.M. with amplitude \[a\sqrt{2}\]

D)

The motion is S.H.M. with amplitude \[2a\]

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4)

The resultant of two rectangular simple harmonic motions of the same frequency and unequal amplitudes but differing in phase by \[\frac{\pi }{2}\] is [BHU 2003; CPMT 2004; MP PMT 1989, 2005; BCECE 2005]

A)

Simple harmonic

B)

Circular

C)

Elliptical

D)

Parabolic

View Solution

5)

The composition of two simple harmonic motions of equal periods at right angle to each other and with a phase difference of \[\pi \] results in the displacement of the particle along [CBSE PMT 1990]

A)

Straight line

B)

Circle

C)

Ellipse

D)

Figure of eight

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6)

Two mutually perpendicular simple harmonic vibrations have same amplitude, frequency and phase. When they superimpose, the resultant form of vibration will be [MP PMT 1992]

A)

A circle

B)

An ellipse

C)

A straight line

D)

A parabola

View Solution

7)

The displacement of a particle varies according to the relation x = 4(cospt + sinpt). The amplitude of the particle is [AIEEE 2003]

A)

8

B)

? 4

C)

4

D)

\[4\sqrt{2}\]

View Solution

8)

A S.H.M. is represented by \[x=5\sqrt{2}(\sin 2\pi t+\cos 2\pi t).\]The amplitude of the S.H.M. is [MH CET 2004]

A)

10 cm

B)

20 cm

C)

\[5\sqrt{2}\]cm

D)

50 cm

View Solution

9)

Resonance is an example of [CBSE PMT 1999; BHU 1999; 2005]

A)

Tuning fork

B)

Forced vibration

C)

Free vibration

D)

Damped vibration

View Solution

10)

In case of a forced vibration, the resonance wave becomes very sharp when the [CBSE PMT 2003]

A)

Restoring force is small

B)

Applied periodic force is small

C)

Quality factor is small

D)

Damping force is small

View Solution

11)

Amplitude of a wave is represented by \[A=\frac{c}{a+b-c}\] Then resonance will occur when [CPMT 1984]

A)

\[b=-c/2\]

B)

b = 0 and a = ? c

C)

\[b=-a/2\]

D)

None of these

View Solution

12)

A particle with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force \[F\sin \omega t\]. If the amplitude of the particle is maximum for \[\omega ={{\omega }_{1}}\] and the energy of the particle is maximum for \[\omega ={{\omega }_{2}}\], then (where w0 natural frequency of oscillation of particle) [CBSE PMT 1998]

A)

\[{{\omega }_{1}}={{\omega }_{0}}\] and \[{{\omega }_{2}}\ne {{\omega }_{o}}\]

B)

\[{{\omega }_{1}}={{\omega }_{0}}\] and \[{{\omega }_{2}}={{\omega }_{o}}\]

C)

\[{{\omega }_{1}}\ne {{\omega }_{0}}\] and \[{{\omega }_{2}}={{\omega }_{o}}\]

D)

\[{{\omega }_{1}}\ne {{\omega }_{0}}\] and \[{{\omega }_{2}}\ne {{\omega }_{o}}\]

View Solution

13)

A simple pendulum is set into vibrations. The bob of the pendulum comes to rest after some time due to [AFMC 2003; JIPMER 1999]

A)

Air friction

B)

Moment of inertia

C)

Weight of the bob

D)

Combination of all the above

View Solution

14)

A simple pendulum oscillates in air with time period T and amplitude A. As the time passes [CPMT 2005]

A)

T and A both decrease

B)

T increases and A is constant

C)

T increases and A decreases

D)

T decreases and A is constant

View Solution

JEE Main & Advanced Physics Simple Harmonic Motion Question Bank

done Superposition of S H M and Resonance Total Questions - 14

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Superposition of S H M and Resonance Total Questions - 14