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
2.1 kgk = ?

A 2.1 kg mass on a spring oscillates with a period of 1.55 s. Find the spring stiffness k.

m = 2.1 kgT = 1.55 s
k = N/m
2.Easy
0.6 kgk = 130 N/m

A 0.6 kg mass on a spring with stiffness 130 N/m oscillates on a frictionless surface. Find the frequency f.

m = 0.6 kgk = 130 N/m
f = Hz
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2 s? Use g = 9.81 m/s². Find L.

T = 2 sg = 9.81 m/s²
L = m
4.Medium
1.4 kgk = 460 N/mA = 14 cmx = 9 cm

A 1.4 kg mass on a spring with k = 460 N/m oscillates on a frictionless surface with an amplitude of 14 cm. Find its speed v when it is 9 cm from equilibrium.

m = 1.4 kgk = 460 N/mA = 14 cmx = 9 cm
v = m/s
5.Hard
mk = 480 N/mA = 11 cmx = 4 cm

A mass on a spring with k = 480 N/m oscillates on a frictionless surface with an amplitude of 11 cm. Find its kinetic energy K when it is 4 cm from equilibrium.

k = 480 N/mA = 11 cmx = 4 cm
K = J
6.Hard
3 kgk = 300 N/m200 m/s

A 20 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 = 300 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 200 m/sM = 3 kgk = 300 N/m
A = cm

Answer key

  1. 1. k = 34.51 N/m
  2. 2. f = 2.343 Hz
  3. 3. L = 0.994 m
  4. 4. v = 1.944 m/s
  5. 5. K = 2.52 J
  6. 6. A = 13.29 cm

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