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 = 300 N/m

A 3.8 kg mass on a spring with stiffness 300 N/m oscillates on a frictionless surface. Find the period T.

m = 3.8 kgk = 300 N/m
T = s
2.Easy
0.7 kgk = 270 N/m

A 0.7 kg mass on a spring with stiffness 270 N/m oscillates on a frictionless surface. Find the period T.

m = 0.7 kgk = 270 N/m
T = s
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
2.7 kgk = 30 N/mA = 17 cmx = 1 cm

A 2.7 kg mass on a spring with k = 30 N/m oscillates on a frictionless surface with an amplitude of 17 cm. Find its speed v when it is 1 cm from equilibrium.

m = 2.7 kgk = 30 N/mA = 17 cmx = 1 cm
v = m/s
5.Hard
t (s)x (cm)t = ?6.8

A body oscillates in simple harmonic motion with period 3.6 s and amplitude 17 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 6.8 cm?

T = 3.6 sA = 17 cmx = 6.8 cm
t = s
6.Hard
1.5 kgk = 1200 N/m400 m/s

A 12 g bullet moving at 400 m/s hits and stays in a 1.5 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1200 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 12 gv = 400 m/sM = 1.5 kgk = 1200 N/m
A = cm

Answer key

  1. 1. T = 0.7071 s
  2. 2. T = 0.3199 s
  3. 3. T = 3.108 s
  4. 4. v = 0.5657 m/s
  5. 5. t = 0.2358 s
  6. 6. A = 11.27 cm

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