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
3.9 kgk = ?

A 3.9 kg mass on a spring oscillates with a period of 1.2 s. Find the spring stiffness k.

m = 3.9 kgT = 1.2 s
k = N/m
2.Easy
4.9 kgk = 110 N/m

A 4.9 kg mass on a spring with stiffness 110 N/m oscillates on a frictionless surface. Find the period T.

m = 4.9 kgk = 110 N/m
T = s
3.Medium
t (s)x (cm)0.25 s

A 3.3 kg mass on a spring with k = 50 N/m is pulled 14 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.25 s (with sign).

m = 3.3 kgk = 50 N/mA = 14 cmt = 0.25 s
x = cm
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
2.5 kgk = 140 N/mA = 20 cm

A 2.5 kg mass on a spring with k = 140 N/m is pulled 20 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.5 kgk = 140 N/mA = 20 cm
E = J
6.Hard
3.7 kgk = 90 N/mA = 13 cm

A 3.7 kg mass on a spring with k = 90 N/m is pulled 13 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.7 kgk = 90 N/mA = 13 cm
vmax = m/s

Answer key

  1. 1. k = 106.9 N/m
  2. 2. T = 1.326 s
  3. 3. x = 7.878 cm
  4. 4. L = 1.315 m
  5. 5. E = 2.8 J
  6. 6. vmax = 0.6412 m/s

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