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
2.1 kgk = ?

A 2.1 kg mass on a spring oscillates with a period of 1.1 s. Find the spring stiffness k.

m = 2.1 kgT = 1.1 s
k = N/m
2.Easy
0.8 kgk19.5 cm

Hanging a 0.8 kg mass on a spring stretches it by 19.5 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 = 0.8 kgx = 19.5 cmg = 9.81 m/s²
T = s
3.Medium
t (s)x (cm)0.45 s

A 0.4 kg mass on a spring with k = 270 N/m is pulled 13 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 0.45 s (with sign).

m = 0.4 kgk = 270 N/mA = 13 cmt = 0.45 s
v = m/s
4.Medium
2.2 kgk = 410 N/mA = 19 cmx = 5 cm

A 2.2 kg mass on a spring with k = 410 N/m oscillates on a frictionless surface with an amplitude of 19 cm. Find its speed v when it is 5 cm from equilibrium.

m = 2.2 kgk = 410 N/mA = 19 cmx = 5 cm
v = m/s
5.Hard
0.9 kgk = 250 N/mA = 19 cm

A 0.9 kg mass on a spring with k = 250 N/m is pulled 19 cm from equilibrium and released. Find its maximum speed vmax.

m = 0.9 kgk = 250 N/mA = 19 cm
vmax = m/s
6.Hard
4 kgk = 1000 N/m100 m/s

A 10 g bullet moving at 100 m/s hits and stays in a 4 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1000 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 10 gv = 100 m/sM = 4 kgk = 1000 N/m
A = cm

Answer key

  1. 1. k = 68.52 N/m
  2. 2. T = 0.8859 s
  3. 3. v = 2.592 m/s
  4. 4. v = 2.502 m/s
  5. 5. vmax = 3.167 m/s
  6. 6. A = 1.579 cm

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