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CBSE · Class 11 · Physics

Oscillations

Standard difficulty · 20 questions · 40 marks

Name: Date: Score: ____ / 40

Show your working for Sections B and C. Answers are on the last page — try every question first!

Section A — Choose the correct answer8 × 1 = 8 marks
1.
A body in SHM has angular frequency 2π/3 rad/s. Its period is:
  1. 1.5 s
  2. 0.33 s
  3. 6 s
  4. 3 s
2.
A particle moves in SHM with amplitude 19 cm and angular frequency 9 rad/s. Its greatest speed is:
  1. 171 cm/s
  2. 1539 cm/s
  3. 2.11 cm/s
  4. 28 cm/s
3.
A mass of 4 kg oscillates on a spring of spring constant 4 N/m. The period is:
  1. 0.5π s
  2. 2π s
  3. 4π s
  4. π s
4.
The period of a simple pendulum of length 0.25 m is (take g = π2 m/s2):
  1. 2 s
  2. 0.5 s
  3. 1 s
  4. 0 s
5.
In simple harmonic motion, the restoring force is proportional to:
  1. the time
  2. the velocity
  3. the displacement, and directed towards the mean position
  4. the square of the displacement
6.
In SHM with amplitude 13 cm and ω = 6 rad/s, the speed when the displacement is 5 cm is:
  1. 48 cm/s
  2. 72 cm/s
  3. 78 cm/s
  4. 30 cm/s
7.
Springs of spring constants 110 N/m and 30 N/m are joined side by side (in parallel). The effective spring constant is:
  1. 140 N/m
  2. 3,300 N/m
  3. 23.57 N/m
  4. 80 N/m
8.
Assertion (A): If the length of a simple pendulum with period 1.5 s is made 16 times, its period becomes 6 s.
Reason (R): The period of a simple pendulum is proportional to its length.
  1. Both A and R are true, and R is the correct explanation of A.
  2. Both A and R are true, but R is not the correct explanation of A.
  3. A is true, but R is false.
  4. A is false, but R is true.
Section B — Short answer8 × 2 = 16 marks
9.
The displacement of a particle is x = 1 sin(2πt + π/3) cm. Find the amplitude, angular frequency, period, frequency and initial phase.
10.
A particle performs SHM with amplitude 14 cm and period 2 s. Find its greatest speed and greatest acceleration (leave π in the answer).
11.
A 324 kg mass hangs on a spring of spring constant 36 N/m. Find the period and frequency of its oscillations.
12.
What length of simple pendulum has a period of 2 s? (Take g = π2 m/s2.)
13.
A block on a spring (k = 700 N/m) oscillates with amplitude 17 cm. Find its total energy, and its kinetic energy when it is 12.75 cm from the mean position.
14.
A 4 kg block is attached to two springs (160 N/m and 140 N/m) side by side (in parallel). Find the effective spring constant and the period of oscillation (2 decimal places; π = 3.14).
15.
A pendulum has a period of 3.5 s on the earth. What is its period on a planet where g is 9 times the earth's?
16.
For x = 34 sin ωt cm, find the displacement when ωt = 5π/6.
Section C — Word problems4 × 4 = 16 marks
17.
A particle moves according to x = 18 cos(πt) cm. Find (a) the amplitude, period and frequency, (b) the greatest speed, (c) the greatest acceleration, (d) its position at t = 0 (leave π in the answers).
18.
A 4 kg block on a spring (k = 100 N/m) oscillates with amplitude 5 cm. Find (a) the total energy, (b) the kinetic and potential energy when the displacement is 4 cm, (c) its speed then (2 decimal places).
19.
A 4 kg block is attached to two springs of 180 N/m and 40 N/m. Find the effective spring constant and the period when the springs are joined (a) in parallel, (b) in series. Which arrangement oscillates faster? (π = 3.14; 2 decimal places)
20.
A seconds pendulum has a period of 2 s. (a) Find its length (take g = π2 m/s2). (b) If its length is increased by 44%, what is the new period? (c) Will a clock using it run fast or slow?
AmbifulWorksheets
Practice that never repeats
CBSE · Class 11 · Physics

Answer key

Oscillations · AW-11P-OSC-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(d) 3 sT = 2π/ω
2(a) 171 cm/sv_max = Aω
3(d) π sT = 2π√(m/k)
4(c) 1 sT = 2π√(l/g) = 2√l
5(c) the displacement, and directed towards the mean position—
6(b) 72 cm/sv = ω√(A2 − x2)
7(a) 140 N/mk = k1 + k2
8(c) A is true, but R is false.A is true: T ∝ √l, so the period becomes 4 times: 6 s. R is false.
9A = 1 cm; ω = 2π rad/s; T = 1 s; f = 1 Hz; phase π/3compare with x = A sin(ωt + φ); T = 2π/ω
1014π cm/s; 14π2 cm/s2ω = 2π/T = π; v_max = Aω; a_max = Aω2
11T = π s; f = 1/π HzT = 2π√(m/k); f = 1/T
121 mT = 2√l, so l = T2/4
13E = 10.12 J; KE = 4.43 JE = ½kA2; KE = ½k(A2 − x2)
14300 N/m; 0.73 sk = k1 + k2; T = 2π√(m/k)
151.17 sT ∝ 1/√g
1617 cmx = 34 sin(5π/6)
17(a) 18 cm, 2 s, 0.5 Hz; (b) 18π cm/s; (c) 18π2 cm/s2; (d) x = 18 cm, at an extreme positionω = 2π/T; v_max = Aω; a_max = Aω2
18(a) 0.125 J; (b) KE 0.045 J, PE 0.08 J; (c) 0.15 m/sE = ½kA2; PE = ½kx2; KE = E − PE
19(a) 220 N/m, T = 0.85 s; (b) 32.73 N/m, T = 2.2 s; the parallel arrangement (stiffer spring, shorter period)parallel k1 + k2; series k1k2/(k1 + k2)
20(a) 1 m; (b) 2.4 s; (c) slow, because each swing takes longerT = 2√l; T ∝ √l