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
1.8 kgk = ?24 cm

Hanging a 1.8 kg mass on a spring stretches it by 24 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 1.8 kgx = 24 cmg = 9.81 m/s²
k = N/m
2.Easy
4.1 kgk = 320 N/m

A 4.1 kg mass on a spring with stiffness 320 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.1 kgk = 320 N/m
f = Hz
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.2 s? Use g = 9.81 m/s². Find L.

T = 1.2 sg = 9.81 m/s²
L = m
4.Medium
t (s)x (cm)0.05 s

A 3.5 kg mass on a spring with k = 310 N/m is pulled 12 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 0.05 s (with sign).

m = 3.5 kgk = 310 N/mA = 12 cmt = 0.05 s
v = m/s
5.Hard
mk = 320 N/mA = 7 cmx = 1 cm

A mass on a spring with k = 320 N/m oscillates on a frictionless surface with an amplitude of 7 cm. Find its kinetic energy K when it is 1 cm from equilibrium.

k = 320 N/mA = 7 cmx = 1 cm
K = J
6.Hard
t (s)x (cm)t = ?3.25

A body oscillates in simple harmonic motion with period 0.5 s and amplitude 13 cm. What is the shortest time t it needs to move from its maximum displacement of 13 cm to a displacement of 3.25 cm?

T = 0.5 sA = 13 cmx = 3.25 cm
t = s

Answer key

  1. 1. k = 73.58 N/m
  2. 2. f = 1.406 Hz
  3. 3. L = 0.3578 m
  4. 4. v = −0.512 m/s
  5. 5. K = 0.768 J
  6. 6. t = 0.1049 s

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