A 2kg mass attached to a spring undergoes a simple harmonic motion (SHM), with a

Question

A 2kg mass attached to a spring undergoes a simple harmonic motion (SHM), with amplitude 1m and period (pi) s. (a) What is the angular frequency w? (b) What is the spring constant k of the spring? (c) What is the maximum velocity of this SHM? (d) At time t = 0 the mass is found to be at its maximum displacement i.e. x(0) = 1m. Write down the equation for x(t) i.e. the position of the mass as a function of time, and sketch x(t) vs. t over 1 period of oscillation making sure that correct amplitude, period and phase can be deduced by anyone who looks at your sketch (i.e. give correct axis labels).

Explanation / Answer

angular frequency w = 2pi/pi = 2

b)sqrt(k/m) = 2 => k = 8

c) by energy conswervation, kA^2/2 = mv^2/2 => max v = sqrt(k/m) = 2

d) x(t) = cos(2t)

x(t) is simply a cosine curve with time axis scaled by factor of 2

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