A cork on the surface of a pond bobs up and down two times per second on ripples

Question

A cork on the surface of a pond bobs up and down two times per second on ripples having a wavelength of 9.60 cm. If the cork is 13.5 m from shore, how long does it take a ripple passing the cork to reach the shore? The position of a 0.30-kg object attached to a spring is described by x = (0.29 m) cos (0.5 pi t). (Assume t is in seconds.) (a) Find the amplitude of the motion. m (b) Find the spring constant. N/m (c) Find the position of the object at t = 0.32 s. (d) Find the object's speed at t = 0.32 s. m/s

Explanation / Answer

solving first question of the page

9

requency=2

wavelength=9.6 cm

velocity=frequency*wavelength=19.2 cm/s

time taken=1350/19.2=70.3 sec

10

Amplitude=0.29

(b)w=0.5*pi=sqrt(k/m)

we got k=0.74 N/m

(c)at t=0.32 sec

x=0.25 m

(d) v=dx/dt=-0.29*0.5*pi*sin(0.5*pi*t)

v=-0.22 m/s

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