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
1.2 kgk = ?13.5 cm

Hanging a 1.2 kg mass on a spring stretches it by 13.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 1.2 kgx = 13.5 cmg = 9.81 m/s²
k = N/m
2.Easy
3.4 kgk = ?

A 3.4 kg mass on a spring oscillates with a period of 2.15 s. Find the spring stiffness k.

m = 3.4 kgT = 2.15 s
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.9 s? Use g = 9.81 m/s². Find L.

T = 2.9 sg = 9.81 m/s²
L = m
4.Medium
1.9 kgk = 190 N/mA = 13 cmx = 1 cm

A 1.9 kg mass on a spring with k = 190 N/m oscillates on a frictionless surface with an amplitude of 13 cm. Find its speed v when it is 1 cm from equilibrium.

m = 1.9 kgk = 190 N/mA = 13 cmx = 1 cm
v = m/s
5.Hard
2.9 kgk = 50 N/mA = 14 cm

A 2.9 kg mass on a spring with k = 50 N/m is pulled 14 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2.9 kgk = 50 N/mA = 14 cm
amax = m/s²
6.Hard
1.7 kgk = 240 N/mA = 17 cm

A 1.7 kg mass on a spring with k = 240 N/m is pulled 17 cm from equilibrium and released. Find its maximum speed vmax.

m = 1.7 kgk = 240 N/mA = 17 cm
vmax = m/s

Answer key

  1. 1. k = 87.2 N/m
  2. 2. k = 29.04 N/m
  3. 3. L = 2.09 m
  4. 4. v = 1.296 m/s
  5. 5. amax = 2.414 m/s²
  6. 6. vmax = 2.02 m/s

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