Horizontal Harmonic motion and Springs

[mmiller39]

Hi all,

I am having difficulty with a question. I would like some guidance.

QUESTION:

A block rests on a frictionless horizontal surface and is attached to a spring. When set into simple harmonic motion, the block oscillates back and forth with an angular frequency of 9.5 rad/s. The drawing shows the position of the block when the spring is unstrained. This position is labeled ''x = 0 m.'' The drawing also shows a small bottle located 0.080 m to the right of this position. The block is pulled to the right, stretching the spring by 0.050 m, and is then thrown to the left. In order for the block to knock over the bottle,it must be thrown with a speed exceeding v0. Ignoring the width of the block, find v0.

http://edugen.wiley.com/edugen/courses/crs1507/art/qb/qu/c10/ch10p_34.gif

http://edugen.wiley.com/edugen/courses/crs1507/art/qb/qu/c10/ch10p_34.gif

MY WORK:

What we know

w = 9.5 rad/s
A1 = .050 m
A2 = .080 m
f = 1.51197 <----- 9.5 = 2pi f solve for f

at this point I don't know how to incorporate an initial velocity. Any help would be greatly appreciated.

Thanks.

 

[OlderDan]

It's not that there are two amplitudes in the problem. There is one amplitude that must be at least .08m and to get that amplitude the block starts from a certain position x_o = .05m with some initial velocity v_o. Think about the energy the block must have to achieve the needed amplitude.