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
4.2 kgk = 350 N/m

A 4.2 kg mass on a spring with stiffness 350 N/m oscillates on a frictionless surface. Find the period T.

m = 4.2 kgk = 350 N/m
T = s
2.Easy
0.3 kgk = 200 N/m

A 0.3 kg mass on a spring with stiffness 200 N/m oscillates on a frictionless surface. Find the frequency f.

m = 0.3 kgk = 200 N/m
f = Hz
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.6 s? Use g = 9.81 m/s². Find L.

T = 1.6 sg = 9.81 m/s²
L = m
4.Medium
4 kgk = 350 N/mA = 4 cmx = 2 cm

A 4 kg mass on a spring with k = 350 N/m oscillates on a frictionless surface with an amplitude of 4 cm. Find its speed v when it is 2 cm from equilibrium.

m = 4 kgk = 350 N/mA = 4 cmx = 2 cm
v = m/s
5.Hard
0.2 kgk = 490 N/mA = 5 cm

A 0.2 kg mass on a spring with k = 490 N/m is pulled 5 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.2 kgk = 490 N/mA = 5 cm
E = J
6.Hard
3.6 kgk = 490 N/mA = 16 cm

A 3.6 kg mass on a spring with k = 490 N/m is pulled 16 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.6 kgk = 490 N/mA = 16 cm
amax = m/s²

Answer key

  1. 1. T = 0.6883 s
  2. 2. f = 4.109 Hz
  3. 3. L = 0.6361 m
  4. 4. v = 0.324 m/s
  5. 5. E = 0.6125 J
  6. 6. amax = 21.78 m/s²

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