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
1.3 kgk = ?4.5 cm

Hanging a 1.3 kg mass on a spring stretches it by 4.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 1.3 kgx = 4.5 cmg = 9.81 m/s²
k = N/m
2.Easy
2.9 kgk = 350 N/m

A 2.9 kg mass on a spring with stiffness 350 N/m oscillates on a frictionless surface. Find the period T.

m = 2.9 kgk = 350 N/m
T = s
3.Medium
3.4 kgk = 180 N/mA = 17 cmx = 15 cm

A 3.4 kg mass on a spring with k = 180 N/m oscillates on a frictionless surface with an amplitude of 17 cm. Find its speed v when it is 15 cm from equilibrium.

m = 3.4 kgk = 180 N/mA = 17 cmx = 15 cm
v = m/s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.9 s? Use g = 9.81 m/s². Find L.

T = 1.9 sg = 9.81 m/s²
L = m
5.Hard
2.1 kgk = 390 N/mA = 15 cm

A 2.1 kg mass on a spring with k = 390 N/m is pulled 15 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2.1 kgk = 390 N/mA = 15 cm
amax = m/s²
6.Hard
2 kgk = 1800 N/m350 m/s

A 20 g bullet moving at 350 m/s hits and stays in a 2 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1800 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 350 m/sM = 2 kgk = 1800 N/m
A = cm

Answer key

  1. 1. k = 283.4 N/m
  2. 2. T = 0.5719 s
  3. 3. v = 0.5821 m/s
  4. 4. L = 0.897 m
  5. 5. amax = 27.86 m/s²
  6. 6. A = 11.61 cm

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