Question

A mass–spring system moves with simple harmonic motion along the x axis between turning points at x = 10x=10 cm and x_2 = 30x ​2 ​​ =30 cm.

Answer 1

A mass-spring system undergoes simple harmonic motion with turning points at x = 10 cm and x2 = 30 cm. The amplitude of the motion is 10 cm.

Step-by-step explanation:

The given question is related to a mass-spring system that undergoes simple harmonic motion. In simple harmonic motion, the object oscillates back and forth around an equilibrium position due to a restoring force provided by the spring. The position of the object varies periodically with amplitude A and period T.

Here, the turning points are provided at x = 10 cm and x2 = 30 cm. The amplitude A can be calculated as half the difference between the turning points, which is A = (x2 - x)/2 = (30 cm - 10 cm)/2 = 10 cm.

1. 
   
3. The amplitude is A = 10 cm.
4. 
   
6. The equilibrium position is x = 0 cm.
7. 
   
9. The turning points are x = 10 cm and x2 = 30 cm.

Answer 2

(I) The momentum of the system is greatest at the point midway between the points X1 and X2; that is X = 20cm. This is because the velocity is maximum at this point. This point is the equilibrium point of the system.

(II) The Kinetic energy of the system is also great at the point midway between the points X1 and X2; X = 20cm

(III) The total energy is greatest at multiple points.

Step-by-step explanation:

The velocity is greatest at the equilibrium position of the system because the forces responsible for the to and fro movement of the system cancel out of balance up at this point. At any point where there is no net force acting, the acceleration is zero. So at this point the velocity of the body is not changing and has a maximum value. As a result the momentum and kinetic energy of the system will be maximum here too since moment = mv and kinetic energy = ½MV²

The total energy is always the sum of the kinetic and potential energy and at various points the values of the potential and kinetic energies vary from zero to maximum but the total energy is always constant. A simple diagramatic illustration will help to understand this concept. Check the attachment below.