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
1.1 kgk = 50 N/m

A 1.1 kg mass on a spring with stiffness 50 N/m oscillates on a frictionless surface. Find the period T.

m = 1.1 kgk = 50 N/m
T = s
2.Easy
3.7 kgk = 20 N/m

A 3.7 kg mass on a spring with stiffness 20 N/m oscillates on a frictionless surface. Find the period T.

m = 3.7 kgk = 20 N/m
T = s
3.Medium
L = 2 mT = 6.98 s

An astronaut on another planet finds that a simple pendulum 2 m long has a period of 6.98 s for small swings. Find the gravitational acceleration g on that planet.

L = 2 mT = 6.98 s
g = m/s²
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.8 s? Use g = 9.81 m/s². Find L.

T = 1.8 sg = 9.81 m/s²
L = m
5.Hard
2.4 kgk = 320 N/mA = 9 cm

A 2.4 kg mass on a spring with k = 320 N/m is pulled 9 cm from equilibrium and released. Find its maximum speed vmax.

m = 2.4 kgk = 320 N/mA = 9 cm
vmax = m/s
6.Hard
1.5 kgk = 150 N/mA = 10 cm

A 1.5 kg mass on a spring with k = 150 N/m is pulled 10 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.5 kgk = 150 N/mA = 10 cm
E = J

Answer key

  1. 1. T = 0.9319 s
  2. 2. T = 2.703 s
  3. 3. g = 1.621 m/s²
  4. 4. L = 0.8051 m
  5. 5. vmax = 1.039 m/s
  6. 6. E = 0.75 J

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