Oscillations Easy Questions and Answers | Page - 1

Oscillations

The composition of two simple harmonic motions of equal periods at right angle to each other and with a phase difference of π results in the displacement of the particle along

1. circle
1. figures of eight
1. straight line
1. ellipse

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x = a sin ωt
and y = b sin (ωt + π) = – b sin ωt
or x = - y or y = - b x
a b a

It is an equation of a straight line.

Correct Option: C

x = a sin ωt
and y = b sin (ωt + π) = – b sin ωt
or x = - y or y = - b x
a b a

It is an equation of a straight line.

The potential energy of a long spring when stretched by 2 cm is U. If the spring is stretched by 8 cm, the potential energy stored in it is

1. 8 U
1. 16 U
1. U / 4
1. 4 U

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The potential energy of a spring = 1 kx²
2

U = 1 k.(2)² = 4 × 1 k
2 2

For x = 8 cm,
Energy stored = 1 k.(8)² = 64 × 1 k
2 2

= 64 × U = 16 U
4

Correct Option: B

The potential energy of a spring = 1 kx²
2

U = 1 k.(2)² = 4 × 1 k
2 2

For x = 8 cm,
Energy stored = 1 k.(8)² = 64 × 1 k
2 2

= 64 × U = 16 U
4

The particle executing simple harmonic motion has a kinetic energy K₀ cos² ω t. The maximum values of the potential energy and the total energy are respectively

1. K₀ / 2 and K₀
1. K₀ and 2K₀
1. K₀ and K₀
1. 0 and 2K₀.

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We have, U + K = E
where, U = potential energy, K = Kinetic energy, E = Total energy.
Also, we know that, in S.H.M., when potential energy is maximum, K.E. is zero and vice-versa.
∴ U_max - 0 = E ⇒ U_max = E
Further,
K.E. = 1 mω² a² cos² ωt
2

But by question , K.E. = K₀ cos² ωt
K₀ = 1 mω² a²
2

Hence, total energy, E = 1 mω² a² = K₀
2

∴ U_max = K₀ & E = K₀

Correct Option: C

We have, U + K = E
where, U = potential energy, K = Kinetic energy, E = Total energy.
Also, we know that, in S.H.M., when potential energy is maximum, K.E. is zero and vice-versa.
∴ U_max - 0 = E ⇒ U_max = E
Further,
K.E. = 1 mω² a² cos² ωt
2

But by question , K.E. = K₀ cos² ωt
K₀ = 1 mω² a²
2

Hence, total energy, E = 1 mω² a² = K₀
2

∴ U_max = K₀ & E = K₀

A particle moving along the X-axis, executes simple harmonic motion then the force acting on it is given by

1. – A kx
1. A cos (kx)
1. A exp (– kx)
1. Akx
  where, A and k are positive constants.

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For simple harmonic motion, F = – Kx.
Here, K = Ak.

Correct Option: A

For simple harmonic motion, F = – Kx.
Here, K = Ak.

Which one of the following is a simple harmonic motion ?

1. Ball bouncing between two rigid vertical walls
1. Particle moving in a circle with uniform speed
1. Wave moving through a string fixed at both ends
1. Earth spinning about its own axis.

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A wave moving through a string fixed at both ends, is a transverse wave formed as a result of simple harmonic motion of particles of the string.

Correct Option: C

A wave moving through a string fixed at both ends, is a transverse wave formed as a result of simple harmonic motion of particles of the string.