Period of a pendulum and a spring: Class 11 practice
A simple pendulum has T = 2π√(L/g), independent of mass and (for small swings) amplitude. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Square roots
The idea behind period of a pendulum and a spring
A simple pendulum has T = 2π√(L/g), independent of mass and (for small swings) amplitude. A mass on a spring has T = 2π√(m/k).
Step-by-step method
- Pick the right formula.
- Use SI units.
- For ratio questions, use T ∝ √L or T ∝ √m.
Worked example 1 (Basic)
Find the period of a 2.6 m simple pendulum (g = 9.8 m/s²).
- T = 2π√(2.6/9.8)
- = 3.236 s
- Answer: 3.236 s
Worked example 2 (Standard)
A 2.5 kg mass oscillates on a spring of k = 116 N/m. Find the period.
- T = 2π√(2.5/116)
- = 0.922 s
- Answer: 0.922 s
Worked example 3 (Challenge)
A pendulum's length is made 4 times. How does its period change?
- T ∝ √L
- New T = √4 = 2 times
- Answer: 2 times
Common mistakes and misconceptions
- Including the bob's mass for a pendulum
- Using √(k/m)
Practice questions
- (Basic) Find the period of a 2.5 m simple pendulum (g = 9.8 m/s²).
- (Basic) Find the period of a 0.4 m simple pendulum (g = 9.8 m/s²).
- (Standard) A 2 kg mass oscillates on a spring of k = 121 N/m. Find the period.
- (Standard) A 4 kg mass oscillates on a spring of k = 150 N/m. Find the period.
- (Challenge) A pendulum's length is made 16 times. How does its period change?
- (Challenge) A pendulum's length is made 9 times. How does its period change?
Answer key with full working
- Q1: T = 2π√(2.5/9.8) → = 3.173 s → Answer: 3.173 s
- Q2: T = 2π√(0.4/9.8) → = 1.269 s → Answer: 1.269 s
- Q3: T = 2π√(2/121) → = 0.808 s → Answer: 0.808 s
- Q4: T = 2π√(4/150) → = 1.026 s → Answer: 1.026 s
- Q5: T ∝ √L → New T = √16 = 4 times → Answer: 4 times
- Q6: T ∝ √L → New T = √9 = 3 times → Answer: 3 times
Syllabus note
This skill is listed under "Oscillations" for Class 11 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is period of a pendulum and a spring in?
"Oscillations", Class 11 Physics (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.