P16_028.PDF

28. (a) We interpret the problem as asking for the equilibrium position; that is, the block is gently lowered

until forces balance (as opposed to being suddenly released and allowed to oscillate). If the amount

the spring is stretched is x , then we examine force-components along the incline surface and ﬁnd

kx = mg sin θ =

x = 14 . 0sin40 . 0 ◦

120

=0 . 075 m

at equilibrium. The calculator is in degrees mode in the above calculation. The distance from the

top of the incline is therefore 0 . 450 + 0 . 75 = 0 . 525 m.

(b) Just as with a vertical spring, the eﬀect of gravity (or one of its components) is simply to shift the

equilibrium position; it does not change the characteristics (such as the period) of simple harmonic

motion. Thus, Eq. 16-13 applies, and we obtain

T =2 π 14 . 0 / 9 . 8

120

=0 . 686 s .

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