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
4.7 kgk = 320 N/m

A 4.7 kg mass on a spring with stiffness 320 N/m oscillates on a frictionless surface. Find the period T.

m = 4.7 kgk = 320 N/m
T = s
2.Easy
5 kgk = ?

A 5 kg mass on a spring oscillates with a period of 0.8 s. Find the spring stiffness k.

m = 5 kgT = 0.8 s
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2 s? Use g = 9.81 m/s². Find L.

T = 2 sg = 9.81 m/s²
L = m
4.Medium
t (s)x (cm)0.8 s

A 1.9 kg mass on a spring with k = 400 N/m is pulled 15 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.8 s (with sign).

m = 1.9 kgk = 400 N/mA = 15 cmt = 0.8 s
x = cm
5.Hard
1.4 kgk = 300 N/mA = 4 cm

A 1.4 kg mass on a spring with k = 300 N/m is pulled 4 cm from equilibrium and released. Find its maximum speed vmax.

m = 1.4 kgk = 300 N/mA = 4 cm
vmax = m/s
6.Hard
0.3 kgk = 230 N/mA = 12 cm

A 0.3 kg mass on a spring with k = 230 N/m is pulled 12 cm from equilibrium and released. Find its maximum speed vmax.

m = 0.3 kgk = 230 N/mA = 12 cm
vmax = m/s

Answer key

  1. 1. T = 0.7615 s
  2. 2. k = 308.4 N/m
  3. 3. L = 0.994 m
  4. 4. x = 8.618 cm
  5. 5. vmax = 0.5855 m/s
  6. 6. vmax = 3.323 m/s

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