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
4.8 kgk = 280 N/m

A 4.8 kg mass on a spring with stiffness 280 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.8 kgk = 280 N/m
f = Hz
2.Easy
5 kgk = ?

A 5 kg mass on a spring oscillates with a period of 0.7 s. Find the spring stiffness k.

m = 5 kgT = 0.7 s
k = N/m
3.Medium
L = 2.4 m

A simple pendulum has a length of 2.4 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.4 mg = 9.81 m/s²
T = s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.9 s? Use g = 9.81 m/s². Find L.

T = 2.9 sg = 9.81 m/s²
L = m
5.Hard
t (s)x (cm)t = ?3

A body oscillates in simple harmonic motion with period 2.4 s and amplitude 10 cm. What is the shortest time t it needs to move from its maximum displacement of 10 cm to a displacement of 3 cm?

T = 2.4 sA = 10 cmx = 3 cm
t = s
6.Hard
0.6 kgk = 50 N/mA = 7 cm

A 0.6 kg mass on a spring with k = 50 N/m is pulled 7 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.6 kgk = 50 N/mA = 7 cm
amax = m/s²

Answer key

  1. 1. f = 1.216 Hz
  2. 2. k = 402.8 N/m
  3. 3. T = 3.108 s
  4. 4. L = 2.09 m
  5. 5. t = 0.4836 s
  6. 6. amax = 5.833 m/s²

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