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
1.9 kgk = 400 N/m

A 1.9 kg mass on a spring with stiffness 400 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.9 kgk = 400 N/m
f = Hz
2.Easy
0.2 kgk = ?

A 0.2 kg mass on a spring oscillates with a period of 1.25 s. Find the spring stiffness k.

m = 0.2 kgT = 1.25 s
k = N/m
3.Medium
t (s)x (cm)0.85 s

A 2.3 kg mass on a spring with k = 370 N/m is pulled 6 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.85 s (with sign).

m = 2.3 kgk = 370 N/mA = 6 cmt = 0.85 s
x = cm
4.Medium
L = 1.7 m

A simple pendulum has a length of 1.7 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.7 mg = 9.81 m/s²
T = s
5.Hard
t (s)x (cm)t = ?16

A body oscillates in simple harmonic motion with period 1.3 s and amplitude 20 cm. What is the shortest time t it needs to move from its maximum displacement of 20 cm to a displacement of 16 cm?

T = 1.3 sA = 20 cmx = 16 cm
t = s
6.Hard
t (s)x (cm)t = ?4.2

A body oscillates in simple harmonic motion with period 2.6 s and amplitude 14 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 4.2 cm?

T = 2.6 sA = 14 cmx = 4.2 cm
t = s

Answer key

  1. 1. f = 2.309 Hz
  2. 2. k = 5.053 N/m
  3. 3. x = −1.278 cm
  4. 4. T = 2.616 s
  5. 5. t = 0.1331 s
  6. 6. t = 0.1261 s

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