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
1.3 kgk = 290 N/m

A 1.3 kg mass on a spring with stiffness 290 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.3 kgk = 290 N/m
f = Hz
2.Easy
2 kgk = ?

A 2 kg mass on a spring makes 20 complete oscillations in 34 s. Find the spring stiffness k.

m = 2 kgN = 20t = 34 s
k = N/m
3.Medium
0.4 kgk = 380 N/mA = 19 cmx = 1 cm

A 0.4 kg mass on a spring with k = 380 N/m oscillates on a frictionless surface with an amplitude of 19 cm. Find its speed v when it is 1 cm from equilibrium.

m = 0.4 kgk = 380 N/mA = 19 cmx = 1 cm
v = m/s
4.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
5.Hard
2.9 kgk = 190 N/mA = 19 cm

A 2.9 kg mass on a spring with k = 190 N/m is pulled 19 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2.9 kgk = 190 N/mA = 19 cm
amax = m/s²
6.Hard
2.5 kgk = 80 N/mA = 3 cm

A 2.5 kg mass on a spring with k = 80 N/m is pulled 3 cm from equilibrium and released. Find its maximum speed vmax.

m = 2.5 kgk = 80 N/mA = 3 cm
vmax = m/s

Answer key

  1. 1. f = 2.377 Hz
  2. 2. k = 27.32 N/m
  3. 3. v = 5.848 m/s
  4. 4. L = 0.6361 m
  5. 5. amax = 12.45 m/s²
  6. 6. vmax = 0.1697 m/s

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