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
2.4 kgk = ?

A 2.4 kg mass on a spring oscillates with a period of 0.65 s. Find the spring stiffness k.

m = 2.4 kgT = 0.65 s
k = N/m
2.Easy
4.7 kgk = ?

A 4.7 kg mass on a spring oscillates with a period of 1.9 s. Find the spring stiffness k.

m = 4.7 kgT = 1.9 s
k = N/m
3.Medium
2.5 kgk = 470 N/mA = 11 cmx = 5 cm

A 2.5 kg mass on a spring with k = 470 N/m oscillates on a frictionless surface with an amplitude of 11 cm. Find its speed v when it is 5 cm from equilibrium.

m = 2.5 kgk = 470 N/mA = 11 cmx = 5 cm
v = m/s
4.Medium
t (s)x (cm)1.4 s

A 2.2 kg mass on a spring with k = 180 N/m is pulled 3 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1.4 s (with sign).

m = 2.2 kgk = 180 N/mA = 3 cmt = 1.4 s
x = cm
5.Hard
1 kgk = 1600 N/m250 m/s

An 8 g bullet moving at 250 m/s hits and stays in a 1 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1600 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 8 gv = 250 m/sM = 1 kgk = 1600 N/m
A = cm
6.Hard
4 kgk = 1400 N/m450 m/s

A 15 g bullet moving at 450 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 = 1400 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 15 gv = 450 m/sM = 4 kgk = 1400 N/m
A = cm

Answer key

  1. 1. k = 224.3 N/m
  2. 2. k = 51.4 N/m
  3. 3. v = 1.343 m/s
  4. 4. x = 2.986 cm
  5. 5. A = 4.98 cm
  6. 6. A = 9.003 cm

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