The car’s oscillation frequency would be \(\sqrt{2}\) times more if stiffer string is used.
Further Explanation:
Simple Harmonic Motion: Simple Harmonic Motion or SHM is a periodic motion in which restoring force always tended towards the mean position or equilibrium position. The periodic motion is that motion which repeats its path after a fixed interval of time. The example of periodic motion is motion of the hands of a clock.
The formula to calculate the angular frequency of the spring with spring constant \(k\) and \(m\) is given as,
\(\boxed{w=\sqrt{\frac{k}{m}}}\)
The angular frequency of the suspension spring is calculated as follows:
\(\begin{aligned}w_{\text{suspension}}&=\sqrt{\frac{k_{\text{suspension}}}{m}}\\&=\sqrt{\frac{k}{m}\end{aligned}\)
The angular frequency of the stiffer spring is calculated as follows:
\(\begin{aligned}w_{\text{stiffer}}&=\sqrt{\frac{k_{\text{stiffer}}}{m}}\\&=\sqrt{\frac{2k}{m}\end{aligned}\)
Therefore, the car’s oscillation frequency would be \(\sqrt{2}\) times more if stiffer string is used.
Learn More:
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Answer Details:
Grade: High School
Subject: Physics
Chapter: Simple Harmonic Motion
Keywords:
Simple harmonic motion, suspension spring, stiffer, angular frequency, motion, force, time period, spring constant, doubled, car, mass, m, bump, oscillates, oscillation frequency, speed bump
