Hello! Would appreciate help with these Qs. I was able to do them but my method was really dodgy and I was wondering if there were any cleaner ways to get the answer, TIA.
8. https://scontent-syd2-1.xx.fbcdn.net/v/t34.0-12/20292544_1281318438660343_551059664_n.jpg?oh=233b0d40e398c397ba0dd0495d4b2e41&oe=5978DB9D
14. https://scontent-syd2-1.xx.fbcdn.net/v/t34.0-12/20292427_1281318735326980_1619569570_n.jpg?oh=2f9c78ead323407dd331b72d0f7daf86&oe=5978A49E
For the first question, we set up our simple harmonic motion as
+C)
This is a general equation, which will describe ANY simple harmonic motion. Now, we want to fill in the constants. We know that
Where T is the period. Thus,
+C)
Now, we know a few things. We can set the 'centre' point to be at the origin (and thus get rid of our +C term), and thus 6cm to the right is just 6cm. First, the initial position of the particles (ie at t=0)
)
Also, the initial velocity of the particle
)
)
We now have two equations, and two unknowns! We can divide our two relations to get
(See that the A term has cancelled out, and sin/cos=tan)
)
)
We can use this in any one of our above equations to find the value of A;
)
From there, you find the relevant max and min velocity and acceleration values as normal! Note that I would recommend using the 'real' values of alpha and A (ie. not the numerical, rounded values). But that's up to you.
Q2 is pretty similar, so won't go through the process again. In future, if you just want to check your method, post your method as well. It may have been perfectly good,.
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