A mass m is attached to a spring. The spring is stretched and then released from

Question

A mass m is attached to a spring. The spring is stretched and then released from rest at time t=0. The diagram shows the position of the mass at equal intervals of time. Frame A corresponds to t=0. The magnitude of the displacement in frames A and E are equal. Using the diagram, answer the following questions:

1. In what frames is the magnitude of the displacement maximum? Explain

2. In what frames is the magnitude of the force maximum? Explain

3. In what frames is the magnitude of the acceleration maximum? Explain

4. In what frames is the magnitude of the velocity maximum? Explain

5.What multiple or fraction of a period is represented by frames A through E? Explain

6. The displacement is written as a function of time as x=Acos(??t)=Acos(2??f?t). Write the velocity as a function of time.

7. Using your expressions for x and v as a function of time, write the kinetic energy K, elastic potential energy U and the total mechanical energy E as a functions of time.

8.Show that the total mechanical energy is constant.

9.In what frames is the potential energy zero? Explain

10.In what frames is the potential energy maximum? Explain

11. Rank the frames in order of decreasing elastic potential energy.

12. In what frames is the kinetic energy zero?

13.In what frames is the kinetic energy maximum?

14. Rank the frames in order of increasing kinetic energy.

Explanation / Answer

1) A,E
2) A,E
3) C,G
4) C,G
5) 1/2 of a period, as it is from maximum one end to other
6) give the function first, your picture is missing.
7) same problem, picture is required
8) add potential and kinetic energy,it will come to be constant, give picture of function
9) C,G
10) A,E
11) A=E>B=D=F>C=G
12) A,E
13) C,G
14) A=E>B=D=F>C=G

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