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
4.6 kgk = 350 N/m

A 4.6 kg mass on a spring with stiffness 350 N/m oscillates on a frictionless surface. Find the period T.

m = 4.6 kgk = 350 N/m
T = s
2.Easy
4.7 kgk = 10 N/m

A 4.7 kg mass on a spring with stiffness 10 N/m oscillates on a frictionless surface. Find the period T.

m = 4.7 kgk = 10 N/m
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.6 s? Use g = 9.81 m/s². Find L.

T = 1.6 sg = 9.81 m/s²
L = m
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.3 s? Use g = 9.81 m/s². Find L.

T = 2.3 sg = 9.81 m/s²
L = m
5.Hard
3.4 kgk = 450 N/mA = 12 cm

A 3.4 kg mass on a spring with k = 450 N/m is pulled 12 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.4 kgk = 450 N/mA = 12 cm
vmax = m/s
6.Hard
1.2 kgk = 220 N/mA = 16 cm

A 1.2 kg mass on a spring with k = 220 N/m is pulled 16 cm from equilibrium and released. Find its maximum speed vmax.

m = 1.2 kgk = 220 N/mA = 16 cm
vmax = m/s

Answer key

  1. 1. T = 0.7203 s
  2. 2. T = 4.308 s
  3. 3. L = 0.6361 m
  4. 4. L = 1.315 m
  5. 5. vmax = 1.381 m/s
  6. 6. vmax = 2.166 m/s

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