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
4.7 kgk = ?

A 4.7 kg mass on a spring oscillates with a period of 1.95 s. Find the spring stiffness k.

m = 4.7 kgT = 1.95 s
k = N/m
2.Easy
1.3 kgk = 230 N/m

A 1.3 kg mass on a spring with stiffness 230 N/m oscillates on a frictionless surface. Find the period T.

m = 1.3 kgk = 230 N/m
T = s
3.Medium
t (s)x (cm)0.25 s

A 3.5 kg mass on a spring with k = 70 N/m is pulled 5 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.25 s (with sign).

m = 3.5 kgk = 70 N/mA = 5 cmt = 0.25 s
x = cm
4.Medium
0.8 kgk = 40 N/mA = 16 cmx = 15 cm

A 0.8 kg mass on a spring with k = 40 N/m oscillates on a frictionless surface with an amplitude of 16 cm. Find its speed v when it is 15 cm from equilibrium.

m = 0.8 kgk = 40 N/mA = 16 cmx = 15 cm
v = m/s
5.Hard
3.5 kgk = 210 N/mA = 2 cm

A 3.5 kg mass on a spring with k = 210 N/m is pulled 2 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.5 kgk = 210 N/mA = 2 cm
vmax = m/s
6.Hard
0.5 kgk = 1300 N/m400 m/s

A 5 g bullet moving at 400 m/s hits and stays in a 0.5 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1300 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 5 gv = 400 m/sM = 0.5 kgk = 1300 N/m
A = cm

Answer key

  1. 1. k = 48.8 N/m
  2. 2. T = 0.4724 s
  3. 3. x = 2.187 cm
  4. 4. v = 0.3937 m/s
  5. 5. vmax = 0.1549 m/s
  6. 6. A = 7.806 cm

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