11%) Problem 5: A mass mt at the end of a spring of spring constant k is undergo

Question

11%) Problem 5: A mass mt at the end of a spring of spring constant k is undergoing simple harmonic oscillations with amplitude 33% Part (a) At what positive value of displacement x in terms ofAis the potential energy 1/9 of the total mechanical energy? 33% Part (b) what fraction of the total mechanical energy is kinetic if the displacement is l/2 the amplitude? 33% Part (c) By what factor does the maximurn kinetic energy change if the amplitude is increased by a factor of 3? Grade Summa Deductions Potential

Explanation / Answer

(a) PE = 1/2 kx^2 = 1/9

x^2 = 2/9k

x = sqrt (2/9k)

x = 1/3 . sqrt (2/k) [answer)

(b) PE = 1/2 kx^2 = 1/2 k (A/2)^2 = 1/2 k A^2/4

PE = 1/8 kA^2

KE = 1-1/8 = 7/8

KE = 7/8 of Total Energy

(c) Vmax = Aw (w = angular frequency)

w = constant

Means if A increased 3 times then V also increased 3 times

KEmax = 1/2 mv^2

KE"max = 1/2 m(3v)2 = 1/2 m (9v^2) = 9/2 mv^2

KEmax/KE"max = 1/9

9 times increase.

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