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
0.2 kgk = ?10 cm

Hanging a 0.2 kg mass on a spring stretches it by 10 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 0.2 kgx = 10 cmg = 9.81 m/s²
k = N/m
2.Easy
3.1 kgk = 70 N/m

A 3.1 kg mass on a spring with stiffness 70 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3.1 kgk = 70 N/m
f = Hz
3.Medium
t (s)x (cm)0.85 s

A 0.8 kg mass on a spring with k = 150 N/m is pulled 11 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 0.85 s (with sign).

m = 0.8 kgk = 150 N/mA = 11 cmt = 0.85 s
v = m/s
4.Medium
L = 2.1 m

A simple pendulum has a length of 2.1 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.1 mg = 9.81 m/s²
T = s
5.Hard
mk = 20 N/mA = 13 cmx = 6 cm

A mass on a spring with k = 20 N/m oscillates on a frictionless surface with an amplitude of 13 cm. Find the energy U stored in the spring when the mass is 6 cm from equilibrium.

k = 20 N/mA = 13 cmx = 6 cm
U = J
6.Hard
t (s)x (cm)t = ?3.3

A body oscillates in simple harmonic motion with period 2.4 s and amplitude 11 cm. What is the shortest time t it needs to move from its maximum displacement of 11 cm to a displacement of 3.3 cm?

T = 2.4 sA = 11 cmx = 3.3 cm
t = s

Answer key

  1. 1. k = 19.62 N/m
  2. 2. f = 0.7563 Hz
  3. 3. v = 1.205 m/s
  4. 4. T = 2.907 s
  5. 5. U = 0.036 J
  6. 6. t = 0.4836 s

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