When the spring is extended by 44.5 cm - 34.0 cm = 10.5 cm = 0.105 m, it exerts a restoring force with magnitude R such that the net force on the mass is
∑ F = R - mg = 0
where mg = weight of the mass = (7.00 kg) g = 68.6 N.
It follows that R = 68.6 N, and by Hooke's law, the spring constant is k such that
k (0.105 m) = 68.6 N ⇒ k = (68.6 N) / (0.105 m) ≈ 653 N/m
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The force equation can easily prove this. F=ma. This states that the force on an object is equal to mass times acceleration. If the mass stays the same and the velocity of the cars increases than that means there is a larger force. This is because in both cases the cars are stopping in almost an instant and the times of the crashes are theoretically identical. Acceleration is the change in velocity over time. If the velocity is higher with the same amount of time than that means there is a higher acceleration. If you plug a higher acceleration into the force equation then you wind up with a higher force and in turn a more damaging collision.
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A. Forced vibrations, such as those between a tuning fork and a large cabinet surface, result in a much lower sound than was produced by the original vibrating body.
