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
3.8 kgk = 50 N/m

A 3.8 kg mass on a spring with stiffness 50 N/m oscillates on a frictionless surface. Find the period T.

m = 3.8 kgk = 50 N/m
T = s
2.Easy
2.4 kgk = ?2.5 cm

Hanging a 2.4 kg mass on a spring stretches it by 2.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 2.4 kgx = 2.5 cmg = 9.81 m/s²
k = N/m
3.Medium
t (s)x (cm)0.45 s

A 3.5 kg mass on a spring with k = 300 N/m is pulled 10 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.45 s (with sign).

m = 3.5 kgk = 300 N/mA = 10 cmt = 0.45 s
x = cm
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.2 s? Use g = 9.81 m/s². Find L.

T = 2.2 sg = 9.81 m/s²
L = m
5.Hard
0.5 kgk = 440 N/mA = 4 cm

A 0.5 kg mass on a spring with k = 440 N/m is pulled 4 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.5 kgk = 440 N/mA = 4 cm
E = J
6.Hard
1.4 kgk = 30 N/mA = 16 cm

A 1.4 kg mass on a spring with k = 30 N/m is pulled 16 cm from equilibrium and released. Find its maximum acceleration amax.

m = 1.4 kgk = 30 N/mA = 16 cm
amax = m/s²

Answer key

  1. 1. T = 1.732 s
  2. 2. k = 941.8 N/m
  3. 3. x = −5.194 cm
  4. 4. L = 1.203 m
  5. 5. E = 0.352 J
  6. 6. amax = 3.429 m/s²

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