# physics

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A simple harmonic oscillator consists of a 1.1 kg block attached to a spring (k = 180 N/m). The block slides on a horizontal frictionless surface about the equilibrium point x = 0 with a total mechanical energy of 3.0 J. (a) What is the amplitude of the oscillation? (b) How many oscillations does the block complete in 15 s? (c) What is the maximum kinetic energy attained by the block? (d) What is the speed of the block at x = 0.14 m?

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(a) The amplitude X is the value for which all energy is potential:
(1/2) k X^2 = 3 Joules

(b) Compute the period P = 2*pi*sqrt(M/k)
Diveide 15s by P for the number of scillations

(c) 3 J, at the equilibrium point where the spring is unstretched.

(d) The speed V at x = 0.14 m can be obtained from
(1/2)k(0.14)^2 + (1/2) M V^2 = 3 J

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