A particle is performing shm has a frequency of 10 per minute.at a distance of 8cm from the mean position it's velocity is 3/5 max velocity.find it's amplitude max acceleration and velocity at a 5 cm from mean position.
Answers
David meant that simply having x = Acos(t) (where x is displacement and t is time) wouldn't be a very god description of every case of simple harmonic oscillation. This is because the period of an oscillator is variable and dependent on the mass and spring constant of the oscillator. Because the period won't be the same for every problem, we have to come up with a more complex definition to use for time.
He gets cos(0) = 1 from trig. If you have an imaginary right triangle (that couldn't exist in real life) with a 0 degree angle, the cosine would be the adjacent over the hypotenuse. Since one angle of this right triangle is 90 degrees and the other is 0 degrees, the third angle must also be 90. Since two angles are the same, the triangle is isosceles and the two 90 degree sides would be the same. If you draw it out in your head, one of the congruent sides is adjacent to the 0 deg angle, and one is the hypotenuse. Thus, when you compute cos(0), you're doing x/x, which is 1.
When it says "as a function of time", the video means that time is the independent variable in this scenario, that's all.
Hope this helps!