Oscillation MCQ: Definition and Explanation

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The term oscillation refers to the continuous to and fro movement of an object between two positions or states. A particle is said to have SHM i.e. simple harmonic motion if it moves to and fro about a fixed point such that its acceleration at any instant is directly proportional to displacement but the direction of acceleration is opposite to the direction of displacement. Example: motion of spring on a frictionless surface when its one end is fixed and other is in motion.

Read Also: Periodic Motion

Ques- The path length of oscillating simple pendulum of length 1 m is 16 cm its max velocity is ( g = π2 m/s2 )

2 π cm/s
4 π cm/s
8 π cm/s
16 π cm/s

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Ans: (C)

Explanation:

(mgl – mgl cosθ) = ½ mv²

mgl ( 1 – cosθ) = ½ mv²

m is cancelled from both sides

2gl ( 1 – cosθ) = v²

2gl sin2θ = v² --------------------------------------- 1 – cosθ = sin²θ

v = √ (2 gl sin²θ)

Multiply and divide by 2

v = √ (4 g l sin²θ)/2

v = 2√ (g l sin²θ)/2

v = 2√ (g l sin²θ/4)

v = 2√ (g l) × sinθ/2

v = 2√ (g l) × θ/2 ------------------ sinθ/2 = θ/2

v = θ√ (g l)

We need to find θ

path length of oscillating simple pendulum

Ques- The distance covered by particle undergoing SHM in one time period is ------------- (Amplitude A)

4 A
Zero
A
2 A

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Ans: (A)

Explanation:

To understand the above problem, observed the figure carefully, in every half movement the particle covers distance A from its original position to right then come again its original position i.e. A +A = 2 A then pendulum goes left and covers distance A then come back its original position and covers distance A i.e. A+A =2A, it means total distance is 4 A

distance covered by particle undergoing SHM

Ques– The dimension of k in equation F = kx is ----------------

[ L⁰ M1 T^-2 ]
[ L² M1 T^-1 ]
[ L² M1 T^-2 ]
[ L⁰ M1 T^-1 ]

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Ans: (A)

Explanation:

F = Force - [ L¹ M¹ T^-2 ]

x – Distance – L¹

F / x = k

k = L⁰ M¹ T^-2

Ques- A particle performing SHM of periodic time ‘T’. The time taken by the particle in moving from means point to half the maximum displacement is ------------ ( Sin 30 = 0.5 )

T / 2
T / 4
T / 8
T / 12

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Ans: (D)

Explanation-

x = A sin ωt (from mean point)

x= A

âÂÂ---------------------->

x = A/2

A/2 = A sin ωt

½ = sin ωt

Sin-1 (1/2) = ωt

π/ 6 = 2π/T × t

t = T/12

Ques- Calculate the spring constant if the spring with 2N force is stretched by 40 cm

-5 N/m
0 N/m
8 N/m
-5 m/N

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Ans: (A)

Explanation-

F = -k x

F / x = -k

2N/0.4 m = -k

k = -5 N/ m

Ques- A particle is moving in a circle with uniform speed its motion is --------------

Periodic and simple harmonic
Periodic but not simple harmonic
Non periodic
None of the above

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Ans: (B)

Explanation-

If the speed of particle is uniform i.e. periodic in motion. But due to the retardation it will not be simple harmonic.

Ques- A small body of mass 0.10 kg is performing SHM of amplitude 1.0 m and period 0.20 S the maximum force acting on it is ...................

98.596 N
985.96 N
100.2 N
76.23 N

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Ans: (A)

Explanation-

F_max = m a_max ----------------- (1)

a_max = Aω²

a_max = 1× (2π / T)²

a_max = 1× (4π² / T²)

a_max = (4π² / 0.2²) ---------------------------- π = 3.14

a_max = 985.9 -------------------- put in (1)

F_max = 0.1 × 985.9

F_max = 98.59 N

Ques- The maximum velocity of particle in SHM is 0.16 m/s and maximum acceleration is 0.64 m/s2 . The amplitude is ------------------------

4×10^-2 m
4×10^-1 m
4×10 m
4×10⁰ m

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Ans: (A)

Explanation –

V_max = A ω --------------------------- (1)

a_max = A ω2 ---------------------------- (2)

Divide (2) by (1)

a_max/ V_max = Aω²/ Aω

ω = 0.64 / 0.16

ω = 4 ................... put in ( 1 )

0.16 = A ×4

A = 0.04

A = 4×10^-2 m

Ques- In a second pendulum mass of bob is 30 g if it is replaced by 90 g mass then its time period will be --------------------

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Ans: (B)

Explanation –

T = 2 π √ ( l / g)

The time period of second pendulum is always 2 sec

In this case you have to remember this condition.

Ques- The maximum velocity of a particle performing linear SHM is 0.16 m/s if its maximum acceleration is 0.64 m/s² . Calculate its period

2 s
1.7 s
1.5 s
1 s

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Ans: (C)

Explanation –

T = 2 π / ω

V_max = A ω --------------------------- (1)

a_max = A ω² ---------------------------- (2)

Divide (2) by (1)

a_max/ V_max = Aω²/ Aω

ω = 0.64 / 0.16

ω = 4

T = 2 π / 4

T = 1.5 s

Ques- Energy of a simple harmonic motion depends upon -----------

1 / ω²
ω
A²
1 / A²

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Ans: (C)

Explanation –

E. = ½ K A²
E. = ½ m ω² A²

From the above equation we can conclude that the energy of a simple harmonic motion depends upon the square of amplitude.

Ques- The SHM of a particle is given by the equation x = 3 sin (ωt + ωt) the amplitude is -------------

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Ans: (C)

Explanation –

To find the amplitude we need to focus on following equation

Displacement (x) = A sin (ωt + ωt)

A is amplitude

A = 3

Ques- If the velocity of a body is half the maximum velocity. Then what is the distance from the mean position?

2 A
√3 / 2 A
A
A / 2

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Ans: (B)

Explanation –

V = ω √(A² – x² )

V/2 = ω √(A² – x² )

Aω/2 = ω √(A² – x² )

A/2 = √(A² – x² )

Squaring both sides

A²/ 4 = (A² – x²)

A²/ 4 - A² = – x²

-3/4 A² = – x²

Negative sign will be canceled

√3 / 2 A = x

Physics Related Links:
Oscillatory Motion	Transverse and Longitudinal Waves
Wave Speed	Wave Power
Period Angular Frequency	Momentum
Frequency	Velocity
Angular Speed	Wave Motion

Oscillation MCQ: Definition and Explanation

CBSE CLASS XII Related Questions

1.
Draw the number of scattered particles versus the scattering angle graph for scattering of alpha particles by a thin foil. Write two important conclusions that can be drawn from this plot.

2.
Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.

3.
A tank is filled with a liquid to a height of \( 12.5 \, \text{m} \). The apparent depth of a needle lying at the bottom of the tank is measured to be \( 9.0 \, \text{m} \). Calculate the speed of light in the liquid.

4.
Suppose a pure Si crystal has \( 5 \times 10^{28} \) atoms per \( \text{m}^3 \). It is doped with \( 5 \times 10^{22} \) atoms per \( \text{m}^3 \) of Arsenic. Calculate majority and minority carrier concentration in the doped silicon. (Given: \( n_i = 1.5 \times 10^{16} \, \text{m}^{-3} \))

5.
If Bohr’s quantization postulate (angular momentum \( = \frac{nh}{2\pi} \)) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why, then, do we never speak of quantization of orbits of planets around the Sun? Explain.

6.
Write the expression for the magnetic field due to a current element in vector form. Consider a 1 cm segment of a wire, centered at the origin, carrying a current of 10 A in positive x-direction. Calculate the magnetic field \( \mathbf{B} \) at a point \( (1 \, \text{m}, 1 \, \text{m}, 0) \).

Similar Physics Concepts

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Oscillation MCQ: Definition and Explanation

CBSE CLASS XII Related Questions

1. Draw the number of scattered particles versus the scattering angle graph for scattering of alpha particles by a thin foil. Write two important conclusions that can be drawn from this plot.

2.Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.

3.A tank is filled with a liquid to a height of \( 12.5 \, \text{m} \). The apparent depth of a needle lying at the bottom of the tank is measured to be \( 9.0 \, \text{m} \). Calculate the speed of light in the liquid.

4.Suppose a pure Si crystal has \( 5 \times 10^{28} \) atoms per \( \text{m}^3 \). It is doped with \( 5 \times 10^{22} \) atoms per \( \text{m}^3 \) of Arsenic. Calculate majority and minority carrier concentration in the doped silicon. (Given: \( n_i = 1.5 \times 10^{16} \, \text{m}^{-3} \))

5. If Bohr’s quantization postulate (angular momentum \( = \frac{nh}{2\pi} \)) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why, then, do we never speak of quantization of orbits of planets around the Sun? Explain.

6.Write the expression for the magnetic field due to a current element in vector form. Consider a 1 cm segment of a wire, centered at the origin, carrying a current of 10 A in positive x-direction. Calculate the magnetic field \( \mathbf{B} \) at a point \( (1 \, \text{m}, 1 \, \text{m}, 0) \).

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Draw the number of scattered particles versus the scattering angle graph for scattering of alpha particles by a thin foil. Write two important conclusions that can be drawn from this plot.

2.
Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.

3.
A tank is filled with a liquid to a height of \( 12.5 \, \text{m} \). The apparent depth of a needle lying at the bottom of the tank is measured to be \( 9.0 \, \text{m} \). Calculate the speed of light in the liquid.

4.
Suppose a pure Si crystal has \( 5 \times 10^{28} \) atoms per \( \text{m}^3 \). It is doped with \( 5 \times 10^{22} \) atoms per \( \text{m}^3 \) of Arsenic. Calculate majority and minority carrier concentration in the doped silicon. (Given: \( n_i = 1.5 \times 10^{16} \, \text{m}^{-3} \))

5.
If Bohr’s quantization postulate (angular momentum \( = \frac{nh}{2\pi} \)) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why, then, do we never speak of quantization of orbits of planets around the Sun? Explain.

6.
Write the expression for the magnetic field due to a current element in vector form. Consider a 1 cm segment of a wire, centered at the origin, carrying a current of 10 A in positive x-direction. Calculate the magnetic field \( \mathbf{B} \) at a point \( (1 \, \text{m}, 1 \, \text{m}, 0) \).