In simple harmonic motion acceleration is proportional to displacement, and a simple pendulum of length L has time period 2π√(L/g), so this Class 11 sheet opens with the SHM condition and the pendulum formula. Amplitude and x = A sin(ωt + φ) appear in the answers.
Key Takeaways
In SHM acceleration is proportional to displacement (Q1).
A pendulum of length L has period 2π√(L/g) (Q2).
Q4 records amplitude among the answers.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.In simple harmonic motion, the acceleration of the particle is proportional to its
(a) Velocity(b) Displacement(c) Force squared(d) Time
2.The time period of a simple pendulum of length L is
(a) 2π√(g/L)(b) 2π√(L/g)(c) 2π√(Lg)(d) π√(L/g)
3.The time period of SHM with angular frequency ω is
(a) 2πω(b) 2π/ω(c) ω/2π(d) 2π²ω
4.The maximum displacement of a particle from its mean position in SHM is called its
(a) Frequency(b) Amplitude(c) Wavelength(d) Period
5.The displacement of a particle in SHM can be written as
(a) x = A sin(ωt + φ)(b) x = A² sin(ωt)(c) x = Aωt(d) x = A cos(2ωt)
6.At the mean position in SHM, the velocity of the particle is
(a) Zero(b) Maximum(c) Half the amplitude(d) Minimum
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Write the time period of a simple pendulum of length L.
8.Define amplitude in simple harmonic motion.
9.Write the relation between angular frequency ω and time period T.
10.Write the expression for the velocity of a particle in SHM at displacement x.
11.At which position is the speed of a particle in SHM maximum?
12.Write the expression for the acceleration of a particle in SHM at displacement x.
13.Define frequency.
14.Write the SI unit of frequency.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.A simple pendulum has a time period of 2 s. What will be its period if the length is made four times?
16.A particle in SHM has amplitude 5 cm and angular frequency 2 rad/s. Find its maximum velocity.
17.Find the time period of a simple pendulum of length 1 m (g = 10 m/s², take π² = 10).
18.A body completes 20 oscillations in 10 s. Find its frequency and its time period.
19.The maximum acceleration of a particle in SHM is 8 m/s² and its amplitude is 2 m. Find its angular frequency.
20.A simple pendulum has a time period of 1 s on Earth. If taken to the Moon where g is 1/6 of its value on Earth, what happens to its period?
Answer Key
1. b) Displacement
2. b) 2π√(L/g)
3. b) 2π/ω
4. b) Amplitude
5. a) x = A sin(ωt + φ)
6. b) Maximum
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
What is acceleration proportional to in SHM?
Displacement, option (b) in this worksheet (Q1).
What is the time period of a simple pendulum?
2π√(L/g), option (b) in this worksheet (Q2).
What is the amplitude of an oscillation?
The maximum displacement — option (b) in this worksheet (Q4).
Stuck on a similar problem? Clear your next doubt instantly with the Doubt Solver.
Browse more free worksheets for CBSE Grade 11.