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 = 10 N/m

A 2.1 kg mass on a spring with stiffness 10 N/m oscillates on a frictionless surface. Find the frequency f.

m = 2.1 kgk = 10 N/m
f = Hz
2.Easy
5 kgk = ?

A 5 kg mass on a spring oscillates with a period of 0.85 s. Find the spring stiffness k.

m = 5 kgT = 0.85 s
k = N/m
3.Medium
0.6 kgk = 20 N/mA = 10 cmx = 8 cm

A 0.6 kg mass on a spring with k = 20 N/m oscillates on a frictionless surface with an amplitude of 10 cm. Find its speed v when it is 8 cm from equilibrium.

m = 0.6 kgk = 20 N/mA = 10 cmx = 8 cm
v = m/s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 0.9 s? Use g = 9.81 m/s². Find L.

T = 0.9 sg = 9.81 m/s²
L = m
5.Hard
0.5 kgk = 800 N/m100 m/s

A 5 g bullet moving at 100 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 = 800 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 5 gv = 100 m/sM = 0.5 kgk = 800 N/m
A = cm
6.Hard
1.4 kgk = 400 N/mA = 5 cm

A 1.4 kg mass on a spring with k = 400 N/m is pulled 5 cm from equilibrium and released. Find its maximum acceleration amax.

m = 1.4 kgk = 400 N/mA = 5 cm
amax = m/s²

Answer key

  1. 1. f = 0.3473 Hz
  2. 2. k = 273.2 N/m
  3. 3. v = 0.3464 m/s
  4. 4. L = 0.2013 m
  5. 5. A = 2.488 cm
  6. 6. amax = 14.29 m/s²

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