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
5 kgk = 250 N/m

A 5 kg mass on a spring with stiffness 250 N/m oscillates on a frictionless surface. Find the period T.

m = 5 kgk = 250 N/m
T = s
2.Easy
4.2 kgk = 230 N/m

A 4.2 kg mass on a spring with stiffness 230 N/m oscillates on a frictionless surface. Find the period T.

m = 4.2 kgk = 230 N/m
T = s
3.Medium
L = 0.7 mT = 1.77 s

An astronaut on another planet finds that a simple pendulum 0.7 m long has a period of 1.77 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.7 mT = 1.77 s
g = m/s²
4.Medium
3.6 kgk = 310 N/mA = 10 cmx = 5 cm

A 3.6 kg mass on a spring with k = 310 N/m oscillates on a frictionless surface with an amplitude of 10 cm. Find its speed v when it is 5 cm from equilibrium.

m = 3.6 kgk = 310 N/mA = 10 cmx = 5 cm
v = m/s
5.Hard
2.7 kgk = 150 N/mA = 7 cm

A 2.7 kg mass on a spring with k = 150 N/m is pulled 7 cm from equilibrium and released. Find its maximum speed vmax.

m = 2.7 kgk = 150 N/mA = 7 cm
vmax = m/s
6.Hard
1.4 kgk = 490 N/mA = 10 cm

A 1.4 kg mass on a spring with k = 490 N/m is pulled 10 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.4 kgk = 490 N/mA = 10 cm
E = J

Answer key

  1. 1. T = 0.8886 s
  2. 2. T = 0.8491 s
  3. 3. g = 8.821 m/s²
  4. 4. v = 0.8036 m/s
  5. 5. vmax = 0.5217 m/s
  6. 6. E = 2.45 J

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