Show that, under an infinitesimal change of coordinates ха — х'а %3d х" + & x"(х), ja the transformed metric satisfies gls (x) — 9aь(х) %3d— в(v, х, + v, x) to first order in

As a pendulum bob swings back and forth several times, the maximum height it reaches becomes less and less. this is because more and more of the pendulum bob's energy is being transformed into a. heat energy b. kinetic energy c. potential energy d. kinetic energy and potential energy

Suppose that 27 j of work is needed to stretch a spring from its natural length of 6 m to a length of 9 m. (a) how much work is needed to stretch the spring from 12 m to 14 m? j (b) how far beyond its natural length will a force of 78 n keep the spring stretched?

This is the number of complete movements of a wave per second.