Science, asked by mishraadyasha613, 7 months ago

a mass is connected to a spring . if it is displaced a little from the rest position it oscilates where the position is given by x= A*sin (wt) where A and W are constants . find the velocity v(t)​

Answers

Answered by Anonymous
4

Explanation:

oscillates in one dimension with the force of the spring acting parallel to the motion:

W

=

x

f

x

i

F

x

d

x

=

x

f

x

i

k

x

d

x

=

[

1

2

k

x

2

]

x

f

x

i

=

[

1

2

k

x

2

f

1

2

k

x

2

i

]

=

[

U

f

U

i

]

=

Δ

U

.

When considering the energy stored in a spring, the equilibrium position, marked as

x

i

=

0.00

m,

is the position at which the energy stored in the spring is equal to zero. When the spring is stretched or compressed a distance x, the potential energy stored in the spring is

U

=

1

2

k

x

2

.

Energy and the Simple Harmonic Oscillator

To study the energy of a simple harmonic oscillator, we need to consider all the forms of energy. Consider the example of a block attached to a spring, placed on a frictionless surface, oscillating in SHM. The potential energy stored in the deformation of the spring is

U

=

1

2

k

x

2

.

In a simple harmonic oscillator, the energy oscillates between kinetic energy of the mass

K

=

1

2

m

v

2

and potential energy

U

=

1

2

k

x

2

stored in the spring. In the

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