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
4.3 kgk = 50 N/m

A 4.3 kg mass on a spring with stiffness 50 N/m oscillates on a frictionless surface. Find the period T.

m = 4.3 kgk = 50 N/m
T = s
2.Easy
2.8 kgk = ?6.5 cm

Hanging a 2.8 kg mass on a spring stretches it by 6.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 2.8 kgx = 6.5 cmg = 9.81 m/s²
k = N/m
3.Medium
L = 0.7 m

A simple pendulum has a length of 0.7 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.7 mg = 9.81 m/s²
T = s
4.Medium
L = 1.9 m

A simple pendulum has a length of 1.9 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.9 mg = 9.81 m/s²
T = s
5.Hard
3.6 kgk = 60 N/mA = 11 cm

A 3.6 kg mass on a spring with k = 60 N/m is pulled 11 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.6 kgk = 60 N/mA = 11 cm
vmax = m/s
6.Hard
t (s)x (cm)t = ?8.4

A body oscillates in simple harmonic motion with period 2.6 s and amplitude 14 cm. What is the shortest time t it needs to move from its maximum displacement of 14 cm to a displacement of 8.4 cm?

T = 2.6 sA = 14 cmx = 8.4 cm
t = s

Answer key

  1. 1. T = 1.843 s
  2. 2. k = 422.6 N/m
  3. 3. T = 1.678 s
  4. 4. T = 2.765 s
  5. 5. vmax = 0.4491 m/s
  6. 6. t = 0.3837 s

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