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
0.8 kgk = 80 N/m

A 0.8 kg mass on a spring with stiffness 80 N/m oscillates on a frictionless surface. Find the period T.

m = 0.8 kgk = 80 N/m
T = s
2.Easy
2.1 kgk = 50 N/m

A 2.1 kg mass on a spring with stiffness 50 N/m oscillates on a frictionless surface. Find the period T.

m = 2.1 kgk = 50 N/m
T = s
3.Medium
3.6 kgk = 500 N/mA = 11 cmx = 4 cm

A 3.6 kg mass on a spring with k = 500 N/m oscillates on a frictionless surface with an amplitude of 11 cm. Find its speed v when it is 4 cm from equilibrium.

m = 3.6 kgk = 500 N/mA = 11 cmx = 4 cm
v = m/s
4.Medium
t (s)x (cm)0.5 s

A 2.5 kg mass on a spring with k = 260 N/m is pulled 11 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.5 s (with sign).

m = 2.5 kgk = 260 N/mA = 11 cmt = 0.5 s
x = cm
5.Hard
mk = 460 N/mA = 15 cmx = 7 cm

A mass on a spring with k = 460 N/m oscillates on a frictionless surface with an amplitude of 15 cm. Find the energy U stored in the spring when the mass is 7 cm from equilibrium.

k = 460 N/mA = 15 cmx = 7 cm
U = J
6.Hard
3 kgk = 700 N/m200 m/s

An 8 g bullet moving at 200 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 = 700 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 8 gv = 200 m/sM = 3 kgk = 700 N/m
A = cm

Answer key

  1. 1. T = 0.6283 s
  2. 2. T = 1.288 s
  3. 3. v = 1.208 m/s
  4. 4. x = 4.148 cm
  5. 5. U = 1.127 J
  6. 6. A = 3.487 cm

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