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.
The resistance of a metal wire at \(20^\circ\text{C}\) is \(1.05\,\Omega\) and at \(100^\circ\text{C}\) is \(1.38\,\Omega\). Determine the temperature coefficient of resistivity of this metal.

3.
A current of \(4.0\,\text{A}\) flows through a wire of length \(1\,\text{m}\) and cross-sectional area \(1.0\,\text{mm}^2\), when a potential difference of \(2\,\text{V}\) is applied across its ends. Calculate the resistivity of the material of the wire.

4.
A square loop of side 0.50 m is placed in a uniform magnetic field of 0.4 T perpendicular to the plane of the loop. The loop is rotated through an angle of $60^\circ$ in 0.2 s. The value of emf induced in the loop will be:

5.
Consider the nuclear reaction \( X \to Y + Z \). Let \( M_x \), \( M_y \), and \( M_z \) be the masses of the three nuclei X, Y, and Z respectively. Then which of the following relations hold true?

6.
Two point charges -Q and Q are located at points (d, 0) and (0, d) respectively, in x-y plane. The electric field E at the origin will be:

Similar Physics Concepts

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Oscillation MCQ: Definition and Explanation

CBSE CLASS XII Related Questions

1.The resistance of a metal wire at \(20^\circ\text{C}\) is \(1.05\,\Omega\) and at \(100^\circ\text{C}\) is \(1.38\,\Omega\). Determine the temperature coefficient of resistivity of this metal.

3.A current of \(4.0\,\text{A}\) flows through a wire of length \(1\,\text{m}\) and cross-sectional area \(1.0\,\text{mm}^2\), when a potential difference of \(2\,\text{V}\) is applied across its ends. Calculate the resistivity of the material of the wire.

4.A square loop of side 0.50 m is placed in a uniform magnetic field of 0.4 T perpendicular to the plane of the loop. The loop is rotated through an angle of $60^\circ$ in 0.2 s. The value of emf induced in the loop will be:

5.Consider the nuclear reaction \( X \to Y + Z \). Let \( M_x \), \( M_y \), and \( M_z \) be the masses of the three nuclei X, Y, and Z respectively. Then which of the following relations hold true?

6.Two point charges -Q and Q are located at points (d, 0) and (0, d) respectively, in x-y plane. The electric field E at the origin will be:

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
The resistance of a metal wire at \(20^\circ\text{C}\) is \(1.05\,\Omega\) and at \(100^\circ\text{C}\) is \(1.38\,\Omega\). Determine the temperature coefficient of resistivity of this metal.

3.
A current of \(4.0\,\text{A}\) flows through a wire of length \(1\,\text{m}\) and cross-sectional area \(1.0\,\text{mm}^2\), when a potential difference of \(2\,\text{V}\) is applied across its ends. Calculate the resistivity of the material of the wire.

4.
A square loop of side 0.50 m is placed in a uniform magnetic field of 0.4 T perpendicular to the plane of the loop. The loop is rotated through an angle of $60^\circ$ in 0.2 s. The value of emf induced in the loop will be:

5.
Consider the nuclear reaction \( X \to Y + Z \). Let \( M_x \), \( M_y \), and \( M_z \) be the masses of the three nuclei X, Y, and Z respectively. Then which of the following relations hold true?

6.
Two point charges -Q and Q are located at points (d, 0) and (0, d) respectively, in x-y plane. The electric field E at the origin will be: