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
2.3 kgk = ?11 cm

Hanging a 2.3 kg mass on a spring stretches it by 11 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 2.3 kgx = 11 cmg = 9.81 m/s²
k = N/m
2.Easy
3.9 kgk = 160 N/m

A 3.9 kg mass on a spring with stiffness 160 N/m oscillates on a frictionless surface. Find the period T.

m = 3.9 kgk = 160 N/m
T = s
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)0.2 s

A 3.9 kg mass on a spring with k = 90 N/m is pulled 6 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.2 s (with sign).

m = 3.9 kgk = 90 N/mA = 6 cmt = 0.2 s
x = cm
5.Hard
2.6 kgk = 70 N/mA = 3 cm

A 2.6 kg mass on a spring with k = 70 N/m is pulled 3 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2.6 kgk = 70 N/mA = 3 cm
amax = m/s²
6.Hard
0.5 kgk = 180 N/m

A 0.5 kg mass is attached to the lower end of an unstretched vertical spring with k = 180 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 0.5 kgk = 180 N/mg = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. k = 205.1 N/m
  2. 2. T = 0.981 s
  3. 3. T = 1.794 s
  4. 4. x = 3.437 cm
  5. 5. amax = 0.8077 m/s²
  6. 6. vmax = 0.517 m/s

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