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
2.9 kgk5.5 cm

Hanging a 2.9 kg mass on a spring stretches it by 5.5 cm. Use g = 9.81 m/s². The mass is then pulled down a little and released. Find the period T of its oscillation.

m = 2.9 kgx = 5.5 cmg = 9.81 m/s²
T = s
2.Easy
2 kgk = 280 N/m

A 2 kg mass on a spring with stiffness 280 N/m oscillates on a frictionless surface. Find the period T.

m = 2 kgk = 280 N/m
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.3 s? Use g = 9.81 m/s². Find L.

T = 2.3 sg = 9.81 m/s²
L = m
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 = ?14.4

A body oscillates in simple harmonic motion with period 1.2 s and amplitude 18 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 14.4 cm?

T = 1.2 sA = 18 cmx = 14.4 cm
t = s
6.Hard
2.1 kgk = 40 N/mA = 11 cm

A 2.1 kg mass on a spring with k = 40 N/m is pulled 11 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2.1 kgk = 40 N/mA = 11 cm
amax = m/s²

Answer key

  1. 1. T = 0.4705 s
  2. 2. T = 0.531 s
  3. 3. L = 1.315 m
  4. 4. L = 2.09 m
  5. 5. t = 0.1771 s
  6. 6. amax = 2.095 m/s²

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