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
1.7 kgk = ?7 cm

Hanging a 1.7 kg mass on a spring stretches it by 7 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 1.7 kgx = 7 cmg = 9.81 m/s²
k = N/m
2.Easy
2.7 kgk = 390 N/m

A 2.7 kg mass on a spring with stiffness 390 N/m oscillates on a frictionless surface. Find the period T.

m = 2.7 kgk = 390 N/m
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.6 s? Use g = 9.81 m/s². Find L.

T = 2.6 sg = 9.81 m/s²
L = m
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.3 s? Use g = 9.81 m/s². Find L.

T = 1.3 sg = 9.81 m/s²
L = m
5.Hard
4 kgk = 280 N/mA = 5 cm

A 4 kg mass on a spring with k = 280 N/m is pulled 5 cm from equilibrium and released. Find its maximum speed vmax.

m = 4 kgk = 280 N/mA = 5 cm
vmax = m/s
6.Hard
2.3 kgk = 460 N/mA = 11 cm

A 2.3 kg mass on a spring with k = 460 N/m is pulled 11 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2.3 kgk = 460 N/mA = 11 cm
amax = m/s²

Answer key

  1. 1. k = 238.2 N/m
  2. 2. T = 0.5228 s
  3. 3. L = 1.68 m
  4. 4. L = 0.4199 m
  5. 5. vmax = 0.4183 m/s
  6. 6. amax = 22 m/s²

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