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
4.9 kgk = 210 N/m

A 4.9 kg mass on a spring with stiffness 210 N/m oscillates on a frictionless surface. Find the period T.

m = 4.9 kgk = 210 N/m
T = s
2.Easy
3.8 kgk = 380 N/m

A 3.8 kg mass on a spring with stiffness 380 N/m oscillates on a frictionless surface. Find the period T.

m = 3.8 kgk = 380 N/m
T = s
3.Medium
t (s)x (cm)1.15 s

A 2.9 kg mass on a spring with k = 240 N/m is pulled 10 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 1.15 s (with sign).

m = 2.9 kgk = 240 N/mA = 10 cmt = 1.15 s
v = m/s
4.Medium
L = 1.3 mT = 2.41 s

An astronaut on another planet finds that a simple pendulum 1.3 m long has a period of 2.41 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.3 mT = 2.41 s
g = m/s²
5.Hard
t (s)x (cm)t = ?10.4

A body oscillates in simple harmonic motion with period 4 s and amplitude 13 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 10.4 cm?

T = 4 sA = 13 cmx = 10.4 cm
t = s
6.Hard
3 kgk = 1600 N/m300 m/s

A 12 g bullet moving at 300 m/s hits and stays in a 3 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1600 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 12 gv = 300 m/sM = 3 kgk = 1600 N/m
A = cm

Answer key

  1. 1. T = 0.9598 s
  2. 2. T = 0.6283 s
  3. 3. v = 0.7831 m/s
  4. 4. g = 8.836 m/s²
  5. 5. t = 0.5903 s
  6. 6. A = 5.186 cm

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