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
3.4 kgk = ?

A 3.4 kg mass on a spring oscillates with a period of 1.7 s. Find the spring stiffness k.

m = 3.4 kgT = 1.7 s
k = N/m
2.Easy
4.5 kgk = 290 N/m

A 4.5 kg mass on a spring with stiffness 290 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.5 kgk = 290 N/m
f = Hz
3.Medium
L = 0.8 m

A simple pendulum has a length of 0.8 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.8 mg = 9.81 m/s²
T = s
4.Medium
t (s)x (cm)1.1 s

A 4 kg mass on a spring with k = 90 N/m is pulled 8 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1.1 s (with sign).

m = 4 kgk = 90 N/mA = 8 cmt = 1.1 s
x = cm
5.Hard
mk = 340 N/mA = 14 cmx = 12 cm

A mass on a spring with k = 340 N/m oscillates on a frictionless surface with an amplitude of 14 cm. Find its kinetic energy K when it is 12 cm from equilibrium.

k = 340 N/mA = 14 cmx = 12 cm
K = J
6.Hard
4 kgk = 300 N/m450 m/s

A 20 g bullet moving at 450 m/s hits and stays in a 4 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 300 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 450 m/sM = 4 kgk = 300 N/m
A = cm

Answer key

  1. 1. k = 46.45 N/m
  2. 2. f = 1.278 Hz
  3. 3. T = 1.794 s
  4. 4. x = 3.873 cm
  5. 5. K = 0.884 J
  6. 6. A = 25.92 cm

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