Question

1. In a simple harmonic motion, the kinetic energy is equal to the elastic potential energy in the position:

a) X = A / 2

b) X = A

c) X = A / (2) 1/2

d) X = (2 ) ^1/2 A

e) X = 0

1.2 The displacement of a particle in a simple harmonic motion is given by: X = 10 cos (20t - π / 3), which of the following. expressions is equivalent:

a) X = 10 cos (20t + π / 3)

b) X = 10 sen (20t - 5π / 6)

c) X = 10 sen (20 t + π / 6)

d) X = 10 cos (20 t + 2π / 3)

Thank you!

Answer 1

1. Suppose spring of mass m and K is spring constant.
Given that the kinetic energy is equal to elastic potential energy.
ie. KE=PE
   {where x is displacement, k is spring constant}
  ....................(1)
Also we know that  
   &  
putting this in equation (1)
  
  

  

2. Given equation of simple harmonic equation is:

Using trigonometry we can rewrite it as-
  
  ........................................................(1)

Now we can check this with all options:
Here option C is currect because
C:

  

which is equivalent to equation (1) so option C is currect.
we can check other options too similaraly which will be differ from this so they are not currect.
For any clarification you can comment in comment box. Thank you.