00:01
So here we can balance the forces using hooks law, the spring constant multiplied by the stretching or the compression of the spring equals the gravitational force.
00:11
The angular frequency, omega squared, equaling k over m, equaling g over delta l.
00:21
And so we can find the oscillation frequency by finding the change in the length of the spring.
00:26
Now, applying the conservation of energy, we initially have some kinetic energy plus some gravitational potential energy, equaling one half multiplied by k, multiplied by delta l plus the amplitude, quantity squared, plus m g multiplied by negative amplitude.
00:58
And here we've used y sub 1 equaling delta l as the block hits.
01:06
And we can say y sub 3 would be equaling to negative a at the bottom.
01:11
And so the spring has been compressed.
01:12
We could say that delta y equals delta l plus the amplitude.
01:19
And so we can say that then v sub 1 squared equaling 2gh.
01:25
Substitute this expression for we can say that then substituting this into here the conservation of energy equation we can then say that that mgh plus mg delta l equals mg over two delta l multiplied by delta l plus a quantity squared plus mg multiply by negative a...