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
2.9 kgk = ?11.5 cm

Hanging a 2.9 kg mass on a spring stretches it by 11.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 2.9 kgx = 11.5 cmg = 9.81 m/s²
k = N/m
2.Easy
1.3 kgk2.5 cm

Hanging a 1.3 kg mass on a spring stretches it by 2.5 cm. Use g = 9.81 m/s². The mass is then pulled down a little and released. Find the period T of its oscillation.

m = 1.3 kgx = 2.5 cmg = 9.81 m/s²
T = s
3.Medium
L = 0.4 m

A simple pendulum has a length of 0.4 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.4 mg = 9.81 m/s²
T = s
4.Medium
t (s)x (cm)0.7 s

A 4 kg mass on a spring with k = 130 N/m is pulled 13 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 0.7 s (with sign).

m = 4 kgk = 130 N/mA = 13 cmt = 0.7 s
v = m/s
5.Hard
3 kgk = 1700 N/m250 m/s

A 12 g bullet moving at 250 m/s hits and stays in a 3 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1700 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 12 gv = 250 m/sM = 3 kgk = 1700 N/m
A = cm
6.Hard
1.2 kgk = 370 N/mA = 7 cm

A 1.2 kg mass on a spring with k = 370 N/m is pulled 7 cm from equilibrium and released. Find its maximum speed vmax.

m = 1.2 kgk = 370 N/mA = 7 cm
vmax = m/s

Answer key

  1. 1. k = 247.4 N/m
  2. 2. T = 0.3172 s
  3. 3. T = 1.269 s
  4. 4. v = 0.5563 m/s
  5. 5. A = 4.192 cm
  6. 6. vmax = 1.229 m/s

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