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
0.2 kgk = ?

A 0.2 kg mass on a spring oscillates with a period of 1.45 s. Find the spring stiffness k.

m = 0.2 kgT = 1.45 s
k = N/m
2.Easy
0.5 kgk = ?14 cm

Hanging a 0.5 kg mass on a spring stretches it by 14 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 0.5 kgx = 14 cmg = 9.81 m/s²
k = N/m
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
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
t (s)x (cm)t = ?3

A body oscillates in simple harmonic motion with period 3.9 s and amplitude 12 cm. What is the shortest time t it needs to move from its maximum displacement of 12 cm to a displacement of 3 cm?

T = 3.9 sA = 12 cmx = 3 cm
t = s
6.Hard
3.8 kgk = 100 N/mA = 18 cm

A 3.8 kg mass on a spring with k = 100 N/m is pulled 18 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.8 kgk = 100 N/mA = 18 cm
vmax = m/s

Answer key

  1. 1. k = 3.755 N/m
  2. 2. k = 35.04 N/m
  3. 3. T = 1.794 s
  4. 4. T = 2.765 s
  5. 5. t = 0.8182 s
  6. 6. vmax = 0.9234 m/s

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