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
3.8 kgk = 380 N/m

A 3.8 kg mass on a spring with stiffness 380 N/m oscillates on a frictionless surface. Find the period T.

m = 3.8 kgk = 380 N/m
T = s
2.Easy
1.8 kgk = ?

A 1.8 kg mass on a spring oscillates with a period of 0.55 s. Find the spring stiffness k.

m = 1.8 kgT = 0.55 s
k = N/m
3.Medium
2.8 kgk = 470 N/mA = 4 cmx = 2 cm

A 2.8 kg mass on a spring with k = 470 N/m oscillates on a frictionless surface with an amplitude of 4 cm. Find its speed v when it is 2 cm from equilibrium.

m = 2.8 kgk = 470 N/mA = 4 cmx = 2 cm
v = m/s
4.Medium
L = 0.2 m

A simple pendulum has a length of 0.2 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.2 mg = 9.81 m/s²
T = s
5.Hard
3.6 kgk = 220 N/mA = 6 cm

A 3.6 kg mass on a spring with k = 220 N/m is pulled 6 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.6 kgk = 220 N/mA = 6 cm
amax = m/s²
6.Hard
t (s)x (cm)t = ?3

A body oscillates in simple harmonic motion with period 2 s and amplitude 12 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 3 cm?

T = 2 sA = 12 cmx = 3 cm
t = s

Answer key

  1. 1. T = 0.6283 s
  2. 2. k = 234.9 N/m
  3. 3. v = 0.4488 m/s
  4. 4. T = 0.8971 s
  5. 5. amax = 3.667 m/s²
  6. 6. t = 0.08043 s

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