energy conservation question ** 10 pts**?

Question

A 0.53 kg mass vibrates according to the equation x = 0.50cos 6.95 t, where x is in meters and t is in seconds. 

My Answers:
Determine the amplitude.
Express your answer using two significant figures.
  A  =0.50 m


Part B
Determine the frequency.
Express your answer using three significant figures.
  f  =1.11  Hz
my answers

Part C
Determine the total energy.
Express your answer using two significant figures.
  E_{&#92;rm total}  =3.2 J

Part D
Determine the kinetic energy when x = 0.30 m.
Express your answer using two significant figures.
 KE  =
	


Part E
Determine the potential energy when x = 0.30 m.
Express your answer using two significant figures.
  PE  =
	


I got everything except for the last two parts.
I know that E=PE-KE  but i can`t seem to find either PE or KE...

T_T · Accepted Answer

Find the time taken for displacement to equal 0.30m.

0.3=0.5cos6.95t
cos6.95t=0.6
6.95t=0.927295218
t=0.1334 seconds

You are only given displacement but you need to find velocity since kinetic energy deals with velocity. Velocity is the derivative of displacement so we must derive x=0.50cos6.95t. This becomes

v=-3.475sin6.95t

We substitute t=0.2668 since this is the time taken for displacement to be 0.3m

v=-3.475sin(6.95*0.1334)
v=-2.78 m/s

Put this into the kinetic energy equation

KE=(1/2)mv^2
KE=(1/2)(0.53)(-2.78)^2
KE=2.05 J

Using E=KE+PE you can find PE. PE is 1.15 J

hello · Answer

Total energy = 3.2 J = KE + PE

To get part D you need the velocity at x = 0.30 m so first find the time at which x = 0.30 m

0.30 = 0.50 cos (6.95 t) so t = 0.13 s  I used radians /s for 6.95 NOT degrees

Now find v (do you know how to take derivatives ??) v = - (0.50 x 6.95) sin(6.95 t )

plug in with t = 0.13 s to find v = 2.73 m/s   and then find K = 1/2 mv^2

Once you have K you can use KE + PE = 3.2 to find PE

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energy conservation question 10 pts?

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