A cart attached to a spring vibrates with an amplitude A. What fraction of the t

Question

A cart attached to a spring vibrates with an amplitude A. What fraction of the total energy of the cart-spring system is elastic potential energy and what fraction is kinetic energy when the cart is at position x = A/2? A cart attached to a spring vibrates with an amplitude A. What fraction of the total energy of the cart-spring system is elastic potential energy and what fraction is kinetic energy when the cart is at position x = A/2? A cart attached to a spring vibrates with an amplitude A. What fraction of the total energy of the cart-spring system is elastic potential energy and what fraction is kinetic energy when the cart is at position x = A/2? A cart attached to a spring vibrates with an amplitude A. What fraction of the total energy of the cart-spring system is elastic potential energy and what fraction is kinetic energy when the cart is at position x = A/2?

Explanation / Answer

KE = EPE when EPE = ½ * max EPE, or
½kx² = ½(½kA/2²)
x² = A²/8
x / A = 1 / 8 0.35/ 1

(2^2-1)/(2^2) = 3/4

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