Springs & pendulums worksheet with answers

Free printable Springs & pendulums worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
2.6 kgk

A 2.6 kg mass on a spring makes 15 complete oscillations in 17 s. Find the frequency f of the oscillation.

m = 2.6 kgN = 15t = 17 s
f = Hz
2.Easy
3.5 kgk = 50 N/m

A 3.5 kg mass on a spring with stiffness 50 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3.5 kgk = 50 N/m
f = Hz
3.Medium
L = 2 m

A simple pendulum has a length of 2 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2 mg = 9.81 m/s²
T = s
4.Medium
t (s)x (cm)0.75 s

A 3 kg mass on a spring with k = 130 N/m is pulled 12 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.75 s (with sign).

m = 3 kgk = 130 N/mA = 12 cmt = 0.75 s
x = cm
5.Hard
1 kgk = 2000 N/m450 m/s

An 8 g bullet moving at 450 m/s hits and stays in a 1 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 2000 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 8 gv = 450 m/sM = 1 kgk = 2000 N/m
A = cm
6.Hard
t (s)x (cm)t = ?12.75

A body oscillates in simple harmonic motion with period 3.6 s and amplitude 17 cm. What is the shortest time t it needs to move from its maximum displacement of 17 cm to a displacement of 12.75 cm?

T = 3.6 sA = 17 cmx = 12.75 cm
t = s

Answer key

  1. 1. f = 0.8824 Hz
  2. 2. f = 0.6015 Hz
  3. 3. T = 2.837 s
  4. 4. x = 2.674 cm
  5. 5. A = 8.018 cm
  6. 6. t = 0.4141 s

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