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
0.7 kgk5.5 cm

Hanging a 0.7 kg mass on a spring stretches it by 5.5 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 = 0.7 kgx = 5.5 cmg = 9.81 m/s²
T = s
2.Easy
0.3 kgk = 120 N/m

A 0.3 kg mass on a spring with stiffness 120 N/m oscillates on a frictionless surface. Find the period T.

m = 0.3 kgk = 120 N/m
T = s
3.Medium
0.2 kgk = 290 N/mA = 17 cmx = 13 cm

A 0.2 kg mass on a spring with k = 290 N/m oscillates on a frictionless surface with an amplitude of 17 cm. Find its speed v when it is 13 cm from equilibrium.

m = 0.2 kgk = 290 N/mA = 17 cmx = 13 cm
v = m/s
4.Medium
t (s)x (cm)1.25 s

A 1.2 kg mass on a spring with k = 250 N/m is pulled 14 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 1.25 s (with sign).

m = 1.2 kgk = 250 N/mA = 14 cmt = 1.25 s
v = m/s
5.Hard
2.5 kgk = 80 N/mA = 8 cm

A 2.5 kg mass on a spring with k = 80 N/m is pulled 8 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.5 kgk = 80 N/mA = 8 cm
E = J
6.Hard
3 kgk = 600 N/m300 m/s

A 15 g bullet moving at 300 m/s hits and stays in a 3 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 600 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 15 gv = 300 m/sM = 3 kgk = 600 N/m
A = cm

Answer key

  1. 1. T = 0.4705 s
  2. 2. T = 0.3142 s
  3. 3. v = 4.171 m/s
  4. 4. v = 1.46 m/s
  5. 5. E = 0.256 J
  6. 6. A = 10.58 cm

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