The position of a 50 g oscillating mass is given by x(t) = (2.0 cm) cos ((10 s^-

Question

The position of a 50 g oscillating mass is given by x(t) = (2.0 cm) cos ((10 s^-1) t), where t is measured in seconds. Determine (i.) The amplitude. (ii.) The period. (iii.) The spring constant. (iv.) The maximum velocity. (v.) The total energy. (vi.) The velocity at t = 0.40 s. (b.) A building is being knocked down with a wrecking ball, which is a big metal sphere that swings on a 10-m-long cable. You are (very unwisely!) standing directly beneath the point from which the wrecking ball is hung when you notice that the ball has just been released and is swinging directly toward you. How much time do you have to move out of the way?

Explanation / Answer

solving first part as second part ia itself a new question

solving first question

x=2cos(10t)

(i)amplitude=2 cm

(ii) w=10

period=2*pi/w=0.63 sec

(iii)w=sqrt(k/m)=10

we got k=100*m=5 N/m

(iv)maximum velocity=wA=0.2 m/s=20 cm/s

(v)Energy=0.5mv^2=1*10^(-3) J

(vi)v=dx/dt=-0.2sin(10t)

at t=0.4 sec

v=0.15 m/s

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