Question

13. A type of cuckoo clock keeps time by having a mass bouncing on a spring, usually something cute like a cherub in a chair. What force constant is needed to produce a period of 0.500 s for a 0.0150-kg mass?
The answer is 2.37N/m but please show your work.

Answer 1

The force constant that is needed to produce a period of 0.500 s for a 0.0150-kg mass is 2.37 N/m

Data obtained from the question

Period (T) = 0.5 s

Mass (m) = 0.015 Kg

Pi (π) = 3.14

Spring constant (K) =?

How to determine the spring constant

The spring constant can be obtained by using the formula for calculating the period of simple harmonic motion. This is illustrated below

T = 2π√(m /K)

Square both side

T² = 4π²m / K

Cross multiply

T² × K = 4π²m

Divide both side by T²

K = 4π²m / T

K = (4 × 3.14² × 0.015) / 0.5²

K = 2.37 N/m

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