A 1.45kg mass oscillates according to the equation x=0.650cos8.10t, where x is in meters and t is in seconds.Determine the amplitude, frequency, total energy,.

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A 0.650-kg mass oscillates according to the equation x=0.25 sin (4.70 t) where x is in meters and is in seconds. Determine (a) the amplitude, (b) the frequency, (c) the period, (d) the total energy, and (e) the kinetic energy and potential energy when x is 15 cm.

Step-by-step solution

1. Step 1 of 7

   (a)

   The equation of the motion is given by,

   The general expression for the equation of the motion is,

   Here, A is the amplitude, is the angular frequency, and t is the time.

   Compare the two equations, we get and.

   Therefore, the amplitude is.

2. Step 2 of 7

   (b)

   Use the angular frequency to find the frequency.

   The expression for the angular frequency is,

   Here, is the frequency.

   Rewrite the equation for f.

   Substitute for.

   Therefore, the frequency is.

3. Step 3 of 7

   (c)

   Use the frequency to find the period.

   The period is the reciprocal of the frequency. That is,

   Substitute for.

   Therefore, the period is.

4. Step 4 of 7

   (d)

   The maximum velocity is defined as,

   The expression for the total energy is,

   Substitute for.

   Substitute for, 0.65 kg for m, and 0.25 m for A.

   Therefore, the total energy is.

5. Step 5 of 7

   Bollywood movies icons download for mac. (e)

   Let k be the spring constant. Thus, the angular frequency in terms of spring constant is,

   Rewrite the equation for.

6. Step 6 of 7
   The expression for the potential energy is,

   Here, k is the spring constant.

   Substitute for.

   Substitutefor, 0.65 kg for m, and 0.15 m for x.

   Therefore, the potential energy is.

7. Step 7 of 7

   The kinetic energy is equal to the difference between the total energy and the potential energy. That is,

   Substitute 0.45 J for and 0.16 J for.

   Therefore, the kinetic energy is.