Question

An object–spring system undergoes simple harmonic motion with an amplitude A. Does the total energy change if the mass is doubled but the amplitude isn’t changed? Are the kinetic and potential energies at a given point in its motion affected by the change in mass? Explain

Answer 1

the total energy does not change if the mass is doubled and the amplitude is constant

B. The kinetic and potential energies at a given point in its motion is not affected by the change in mass

Step-by-step explanation:

`E=(1)/(2) *kA^{2)`

The total energy stored by an object-spring balance is the equation above

E= Energy stored in the spring

k= spring constant

A= amplitude

if the mass is doubled ,and amplitude remains constant the energy does not change

also
`E=(1)/(2) kx^(2) +(1)/(2) mv^(2)`

The total energy is given by the above. if the mass is doubled, the sum of the potential energy and kinetic energy remains the same at a given point and can't be affected by the change

x=displacement from equilibrium

v=velocity of the object

k= spring constant

m=mass of the object