16.5 Energy and the Simple Harmonic Oscillator

Why does it hurt more if your hand is snapped with a ruler than with a loose spring, even if the displacement of each system is equal?

You are observing a simple harmonic oscillator. Identify one way you could decrease the maximum velocity of the system.

A mass of 1 kg undergoes simple harmonic motion with amplitude of 1 m. If the period of the oscillation is 1 s, calculate the internal energy of the system.

The length of nylon rope from which a mountain climber is suspended has a force constant of $1.40 \times 10^{4} \text{N}/\text{m}$

(a) What is the frequency at which he bounces, given his mass plus and the mass of his equipment are 90.0 kg? Ignore the change in gravitational potential energy after the cord begins to stretch.

(b) How much would this rope stretch to break the climber’s fall if he free-falls 2.00 m before the rope runs…

Near the top of the Citigroup Center building in New York City, there is an object with mass of $4 . \text{00} \times \text{10}^{5} \text{kg}$ on springs that have adjustable force constants. Its function is to dampen wind-driven oscillations of the building by oscillating at the same frequency as the building is being driven—the driving force is transferred to the object, which oscillates instead of the entire building. (a) What effective…