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
3.5 kgk = 100 N/m

A 3.5 kg mass on a spring with stiffness 100 N/m oscillates on a frictionless surface. Find the period T.

m = 3.5 kgk = 100 N/m
T = s
2.Easy
1.2 kgk = ?

A 1.2 kg mass on a spring makes 25 complete oscillations in 55 s. Find the spring stiffness k.

m = 1.2 kgN = 25t = 55 s
k = N/m
3.Medium
L = 1.3 mT = 5.63 s

An astronaut on another planet finds that a simple pendulum 1.3 m long has a period of 5.63 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.3 mT = 5.63 s
g = m/s²
4.Medium
L = 0.3 m

A simple pendulum has a length of 0.3 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.3 mg = 9.81 m/s²
T = s
5.Hard
2.5 kgk = 490 N/mA = 6 cm

A 2.5 kg mass on a spring with k = 490 N/m is pulled 6 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2.5 kgk = 490 N/mA = 6 cm
amax = m/s²
6.Hard
t (s)x (cm)t = ?6.75

A body oscillates in simple harmonic motion with period 1.3 s and amplitude 9 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 6.75 cm?

T = 1.3 sA = 9 cmx = 6.75 cm
t = s

Answer key

  1. 1. T = 1.175 s
  2. 2. k = 9.788 N/m
  3. 3. g = 1.619 m/s²
  4. 4. T = 1.099 s
  5. 5. amax = 11.76 m/s²
  6. 6. t = 0.1755 s

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