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
4.7 kgk = 260 N/m

A 4.7 kg mass on a spring with stiffness 260 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.7 kgk = 260 N/m
f = Hz
2.Easy
2.4 kgk = ?

A 2.4 kg mass on a spring oscillates with a period of 0.65 s. Find the spring stiffness k.

m = 2.4 kgT = 0.65 s
k = N/m
3.Medium
2.1 kgk = 110 N/mA = 5 cmx = 4 cm

A 2.1 kg mass on a spring with k = 110 N/m oscillates on a frictionless surface with an amplitude of 5 cm. Find its speed v when it is 4 cm from equilibrium.

m = 2.1 kgk = 110 N/mA = 5 cmx = 4 cm
v = m/s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.1 s? Use g = 9.81 m/s². Find L.

T = 2.1 sg = 9.81 m/s²
L = m
5.Hard
3.7 kgk = 210 N/mA = 12 cm

A 3.7 kg mass on a spring with k = 210 N/m is pulled 12 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 3.7 kgk = 210 N/mA = 12 cm
E = J
6.Hard
mk = 330 N/mA = 18 cmx = 1 cm

A mass on a spring with k = 330 N/m oscillates on a frictionless surface with an amplitude of 18 cm. Find its kinetic energy K when it is 1 cm from equilibrium.

k = 330 N/mA = 18 cmx = 1 cm
K = J

Answer key

  1. 1. f = 1.184 Hz
  2. 2. k = 224.3 N/m
  3. 3. v = 0.2171 m/s
  4. 4. L = 1.096 m
  5. 5. E = 1.512 J
  6. 6. K = 5.329 J

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