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
1.6 kgk = ?

A 1.6 kg mass on a spring oscillates with a period of 2.35 s. Find the spring stiffness k.

m = 1.6 kgT = 2.35 s
k = N/m
2.Easy
0.5 kgk13 cm

Hanging a 0.5 kg mass on a spring stretches it by 13 cm. Use g = 9.81 m/s². The mass is then pulled down a little and released. Find the period T of its oscillation.

m = 0.5 kgx = 13 cmg = 9.81 m/s²
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.8 s? Use g = 9.81 m/s². Find L.

T = 1.8 sg = 9.81 m/s²
L = m
4.Medium
t (s)x (cm)1 s

A 2 kg mass on a spring with k = 130 N/m is pulled 4 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 1 s (with sign).

m = 2 kgk = 130 N/mA = 4 cmt = 1 s
v = m/s
5.Hard
3 kgk = 50 N/mA = 20 cm

A 3 kg mass on a spring with k = 50 N/m is pulled 20 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 3 kgk = 50 N/mA = 20 cm
E = J
6.Hard
2.5 kgk = 120 N/mA = 6 cm

A 2.5 kg mass on a spring with k = 120 N/m is pulled 6 cm from equilibrium and released. Find its maximum speed vmax.

m = 2.5 kgk = 120 N/mA = 6 cm
vmax = m/s

Answer key

  1. 1. k = 11.44 N/m
  2. 2. T = 0.7233 s
  3. 3. L = 0.8051 m
  4. 4. v = −0.3155 m/s
  5. 5. E = 1 J
  6. 6. vmax = 0.4157 m/s

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