Use dimensional analysis to obtain the SI unit of k in terms of fundamental quantities in the expression below. a is the acceleration, x is the displacement, m is the mass of the oscillating object, and k is the spring constant

 

A mass m is connected to a spring of spring constant k . The
mass sits on a frictionless horizontal surface and the spring isconnected to a wall. Thus the mass
spring system can undergo oscillations in the horizontal direction.At t=0 the mass has velocity
Vo , in the pos x-direction and the spring is stretched a distanceL/2 . Answer the following in
terms of quantities given or a subset thereof.

(a) What is the energy of the system?
(b) What is the distance of maximum displacement of thespring?
(c) Write down an expression for the position of the mass as afunction of time. You need the amplitude of the oscillations andthe phase.

The position of a particle moving under uniform acceleration is some function of time and the acceleration. Suppose we write this position s = k(a^m)(t^n), where k is a dimensionless constant. Show by dimensional analysis that this expression is satisfied if m = 1 and n = 2. Can this analysis give the value of k?