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
2.2 kgk = ?12 cm

Hanging a 2.2 kg mass on a spring stretches it by 12 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 2.2 kgx = 12 cmg = 9.81 m/s²
k = N/m
2.Easy
3.3 kgk = 30 N/m

A 3.3 kg mass on a spring with stiffness 30 N/m oscillates on a frictionless surface. Find the period T.

m = 3.3 kgk = 30 N/m
T = s
3.Medium
t (s)x (cm)1.05 s

A 2.1 kg mass on a spring with k = 370 N/m is pulled 3 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1.05 s (with sign).

m = 2.1 kgk = 370 N/mA = 3 cmt = 1.05 s
x = cm
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.4 s? Use g = 9.81 m/s². Find L.

T = 2.4 sg = 9.81 m/s²
L = m
5.Hard
0.3 kgk = 300 N/mA = 18 cm

A 0.3 kg mass on a spring with k = 300 N/m is pulled 18 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.3 kgk = 300 N/mA = 18 cm
E = J
6.Hard
3.6 kgk = 450 N/mA = 12 cm

A 3.6 kg mass on a spring with k = 450 N/m is pulled 12 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 3.6 kgk = 450 N/mA = 12 cm
E = J

Answer key

  1. 1. k = 179.9 N/m
  2. 2. T = 2.084 s
  3. 3. x = 0.5954 cm
  4. 4. L = 1.431 m
  5. 5. E = 4.86 J
  6. 6. E = 3.24 J

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