When a mass of 25 g is attached to a certain spring, it makes 20 complete vibrations in 4.0 s. what is the spring constant of th

Question

Black_prince

3 months ago

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When a mass of 25 g is attached to a certain spring, it makes 20 complete vibrations in 4.0 s. what is the spring constant of th

e spring? include units, no spaces. round to two significant figures?

Physics

2 answers:

Keith_Richards [3.2K] · Answer 1 · 2026-02-25T23:49:59+03:00

The system undergoes 20 full vibrations within a 4-second interval, resulting in a frequency of
$f= \frac{20}{4.0 s}=5.0 Hz$

The angular frequency can be determined as
$\omega = 2 \pi f = 2 \pi (5.0 Hz)=31.4 rad/s$

In simple harmonic motion, the angular frequency is also described by
$\omega = \sqrt{ \frac{k}{m} }$
where k represents the spring constant, and m=25 g is equivalent to 0.025 kg, the mass connected to the spring. Utilizing the previously calculated angular frequency, we can establish the value of k:
$k=\omega^2 m=(31.4 rad/s)^2 (0.025 kg)=25 N/m$