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
0.6 kgk = ?

A 0.6 kg mass on a spring oscillates with a period of 1 s. Find the spring stiffness k.

m = 0.6 kgT = 1 s
k = N/m
2.Easy
0.7 kgk = 290 N/m

A 0.7 kg mass on a spring with stiffness 290 N/m oscillates on a frictionless surface. Find the period T.

m = 0.7 kgk = 290 N/m
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.8 s? Use g = 9.81 m/s². Find L.

T = 1.8 sg = 9.81 m/s²
L = m
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.9 s? Use g = 9.81 m/s². Find L.

T = 1.9 sg = 9.81 m/s²
L = m
5.Hard
3.1 kgk = 70 N/mA = 9 cm

A 3.1 kg mass on a spring with k = 70 N/m is pulled 9 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.1 kgk = 70 N/mA = 9 cm
vmax = m/s
6.Hard
2.7 kgk = 450 N/mA = 6 cm

A 2.7 kg mass on a spring with k = 450 N/m is pulled 6 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2.7 kgk = 450 N/mA = 6 cm
amax = m/s²

Answer key

  1. 1. k = 23.69 N/m
  2. 2. T = 0.3087 s
  3. 3. L = 0.8051 m
  4. 4. L = 0.897 m
  5. 5. vmax = 0.4277 m/s
  6. 6. amax = 10 m/s²

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