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 1.5 s. Find the spring stiffness k.

m = 2.1 kgT = 1.5 s
k = N/m
2.Easy
2.1 kgk = 220 N/m

A 2.1 kg mass on a spring with stiffness 220 N/m oscillates on a frictionless surface. Find the period T.

m = 2.1 kgk = 220 N/m
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.2 s? Use g = 9.81 m/s². Find L.

T = 2.2 sg = 9.81 m/s²
L = m
4.Medium
3.6 kgk = 270 N/mA = 13 cmx = 10 cm

A 3.6 kg mass on a spring with k = 270 N/m oscillates on a frictionless surface with an amplitude of 13 cm. Find its speed v when it is 10 cm from equilibrium.

m = 3.6 kgk = 270 N/mA = 13 cmx = 10 cm
v = m/s
5.Hard
2.7 kgk = 40 N/mA = 11 cm

A 2.7 kg mass on a spring with k = 40 N/m is pulled 11 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.7 kgk = 40 N/mA = 11 cm
E = J
6.Hard
1.4 kgk = 210 N/mA = 19 cm

A 1.4 kg mass on a spring with k = 210 N/m is pulled 19 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.4 kgk = 210 N/mA = 19 cm
E = J

Answer key

  1. 1. k = 36.85 N/m
  2. 2. T = 0.6139 s
  3. 3. L = 1.203 m
  4. 4. v = 0.7194 m/s
  5. 5. E = 0.242 J
  6. 6. E = 3.79 J

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