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
3 kgk21 cm

Hanging a 3 kg mass on a spring stretches it by 21 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 = 3 kgx = 21 cmg = 9.81 m/s²
T = s
2.Easy
2.6 kgk = 70 N/m

A 2.6 kg mass on a spring with stiffness 70 N/m oscillates on a frictionless surface. Find the period T.

m = 2.6 kgk = 70 N/m
T = s
3.Medium
t (s)x (cm)1.1 s

A 0.7 kg mass on a spring with k = 170 N/m is pulled 9 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1.1 s (with sign).

m = 0.7 kgk = 170 N/mA = 9 cmt = 1.1 s
x = cm
4.Medium
4 kgk = 120 N/mA = 5 cmx = 1 cm

A 4 kg mass on a spring with k = 120 N/m oscillates on a frictionless surface with an amplitude of 5 cm. Find its speed v when it is 1 cm from equilibrium.

m = 4 kgk = 120 N/mA = 5 cmx = 1 cm
v = m/s
5.Hard
1.2 kgk = 160 N/mA = 2 cm

A 1.2 kg mass on a spring with k = 160 N/m is pulled 2 cm from equilibrium and released. Find its maximum speed vmax.

m = 1.2 kgk = 160 N/mA = 2 cm
vmax = m/s
6.Hard
1.5 kgk = 300 N/m350 m/s

A 10 g bullet moving at 350 m/s hits and stays in a 1.5 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 300 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 10 gv = 350 m/sM = 1.5 kgk = 300 N/m
A = cm

Answer key

  1. 1. T = 0.9193 s
  2. 2. T = 1.211 s
  3. 3. x = −1.225 cm
  4. 4. v = 0.2683 m/s
  5. 5. vmax = 0.2309 m/s
  6. 6. A = 16.44 cm

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