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
0.5 kgk = 200 N/m

A 0.5 kg mass on a spring with stiffness 200 N/m oscillates on a frictionless surface. Find the period T.

m = 0.5 kgk = 200 N/m
T = s
2.Easy
4.5 kgk = 180 N/m

A 4.5 kg mass on a spring with stiffness 180 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.5 kgk = 180 N/m
f = Hz
3.Medium
L = 2.8 m

A simple pendulum has a length of 2.8 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.8 mg = 9.81 m/s²
T = s
4.Medium
L = 1.5 m

A simple pendulum has a length of 1.5 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.5 mg = 9.81 m/s²
T = s
5.Hard
t (s)x (cm)t = ?9.6

A body oscillates in simple harmonic motion with period 2.7 s and amplitude 16 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 9.6 cm?

T = 2.7 sA = 16 cmx = 9.6 cm
t = s
6.Hard
0.2 kgk = 240 N/mA = 18 cm

A 0.2 kg mass on a spring with k = 240 N/m is pulled 18 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.2 kgk = 240 N/mA = 18 cm
E = J

Answer key

  1. 1. T = 0.3142 s
  2. 2. f = 1.007 Hz
  3. 3. T = 3.357 s
  4. 4. T = 2.457 s
  5. 5. t = 0.2765 s
  6. 6. E = 3.888 J

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