Example 1 · level 1
A 2 kg mass hangs from a spring of force constant 200 N/m. Find the period of its vertical oscillations (in s, correct to 2 decimal places). Use π = 3.1416.
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- T = 2π√(2/200) = 2π × 0.1 = 0.63 s.
Answer: 0.63 s
CLASS 11–12 PHYSICS · OSCILLATIONS
Simple harmonic motion: spring and pendulum
Spring–mass: T = 2π√(m/k). Simple pendulum (small swings): T = 2π√(L/g). Frequency f = 1/T.
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Worked examples
Example 2 · level 2
A simple pendulum of length 0.5 m swings with small amplitude in a lab at Surat. Find its period (in s, correct to 2 decimal places). Take g = 9.8 m/s², π = 3.1416.
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- T = 2π√(0.5/9.8) = 1.42 s.
Answer: 1.42 s
Example 3 · level 3
A mass on a spring oscillates with period 2 s. If the mass is made 9 times, what is the new period (in s)?
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- T′ = 2 × √9 = 6 s.
Answer: 6 s