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
0.8 kgk = 80 N/m

A 0.8 kg mass on a spring with stiffness 80 N/m oscillates on a frictionless surface. Find the frequency f.

m = 0.8 kgk = 80 N/m
f = Hz
2.Easy
2.9 kgk = 80 N/m

A 2.9 kg mass on a spring with stiffness 80 N/m oscillates on a frictionless surface. Find the frequency f.

m = 2.9 kgk = 80 N/m
f = Hz
3.Medium
t (s)x (cm)1.15 s

A 2.2 kg mass on a spring with k = 350 N/m is pulled 4 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1.15 s (with sign).

m = 2.2 kgk = 350 N/mA = 4 cmt = 1.15 s
x = cm
4.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
5.Hard
2.7 kgk = 30 N/mA = 10 cm

A 2.7 kg mass on a spring with k = 30 N/m is pulled 10 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.7 kgk = 30 N/mA = 10 cm
E = J
6.Hard
2.8 kgk = 110 N/mA = 16 cm

A 2.8 kg mass on a spring with k = 110 N/m is pulled 16 cm from equilibrium and released. Find its maximum speed vmax.

m = 2.8 kgk = 110 N/mA = 16 cm
vmax = m/s

Answer key

  1. 1. f = 1.592 Hz
  2. 2. f = 0.8359 Hz
  3. 3. x = −1.439 cm
  4. 4. T = 1.794 s
  5. 5. E = 0.15 J
  6. 6. vmax = 1.003 m/s

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