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
0.5 kgk = ?

A 0.5 kg mass on a spring oscillates with a period of 0.3 s. Find the spring stiffness k.

m = 0.5 kgT = 0.3 s
k = N/m
2.Easy
1.5 kgk = ?

A 1.5 kg mass on a spring makes 25 complete oscillations in 54 s. Find the spring stiffness k.

m = 1.5 kgN = 25t = 54 s
k = N/m
3.Medium
t (s)x (cm)1.2 s

A 2.9 kg mass on a spring with k = 360 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 = 1.2 s (with sign).

m = 2.9 kgk = 360 N/mA = 15 cmt = 1.2 s
x = cm
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.8 s? Use g = 9.81 m/s². Find L.

T = 2.8 sg = 9.81 m/s²
L = m
5.Hard
3 kgk = 490 N/m

A 3 kg mass is attached to the lower end of an unstretched vertical spring with k = 490 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 3 kgk = 490 N/mg = 9.81 m/s²
vmax = m/s
6.Hard
0.8 kgk = 290 N/m

A 0.8 kg mass is attached to the lower end of an unstretched vertical spring with k = 290 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 0.8 kgk = 290 N/mg = 9.81 m/s²
xmax = cm

Answer key

  1. 1. k = 219.3 N/m
  2. 2. k = 12.69 N/m
  3. 3. x = 10.41 cm
  4. 4. L = 1.948 m
  5. 5. vmax = 0.7676 m/s
  6. 6. xmax = 5.412 cm

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