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 = 250 N/m

A 4.8 kg mass on a spring with stiffness 250 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.8 kgk = 250 N/m
f = Hz
2.Easy
2.8 kgk = ?22 cm

Hanging a 2.8 kg mass on a spring stretches it by 22 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 2.8 kgx = 22 cmg = 9.81 m/s²
k = N/m
3.Medium
t (s)x (cm)0.6 s

A 2.2 kg mass on a spring with k = 40 N/m is pulled 9 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 0.6 s (with sign).

m = 2.2 kgk = 40 N/mA = 9 cmt = 0.6 s
v = m/s
4.Medium
0.8 kgk = 360 N/mA = 5 cmx = 3 cm

A 0.8 kg mass on a spring with k = 360 N/m oscillates on a frictionless surface with an amplitude of 5 cm. Find its speed v when it is 3 cm from equilibrium.

m = 0.8 kgk = 360 N/mA = 5 cmx = 3 cm
v = m/s
5.Hard
mk = 130 N/mA = 9 cmx = 4 cm

A mass on a spring with k = 130 N/m oscillates on a frictionless surface with an amplitude of 9 cm. Find the energy U stored in the spring when the mass is 4 cm from equilibrium.

k = 130 N/mA = 9 cmx = 4 cm
U = J
6.Hard
t (s)x (cm)t = ?12

A body oscillates in simple harmonic motion with period 0.7 s and amplitude 15 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 12 cm?

T = 0.7 sA = 15 cmx = 12 cm
t = s

Answer key

  1. 1. f = 1.149 Hz
  2. 2. k = 124.9 N/m
  3. 3. v = −0.2113 m/s
  4. 4. v = 0.8485 m/s
  5. 5. U = 0.104 J
  6. 6. t = 0.1033 s

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