Physics [Vibrations]

[匿名]

2009-04-01 7:44 am

A prison performs simple harmonic motion along a horizontal straight line. Lt completes three complete oscillation per minute. The situation is as illustrated in Figure 1.

a)What is its angular frequencyω?

b)If the mass of the prison is 18 kg, what is its force constant k?

c)Furthermore, if its maximum speed is 30 x 10^-3 ms^-1, What is its total energy for this harmonic motion?

d)When its displacement from its equilibrium position is 80 x 10^-3m, what is the speed of prison?

Link of the figure 1
http://s582.photobucket.com/albums/ss266/fn14829/?action=view&current=0001.jpg

回答 (1)

Prof. Physics

2009-04-01 4:31 pm

✔ 最佳答案

a. Period, T = 60 / 3 = 20 s

By T = 2pi / ω

20 = 2pi / ω

Angular frequency, ω = 0.314 rads-1

b. By T = 2pi(m / k)1/2

20 = 2pi(18 / k)1/2

Spring constant, k = 1.78 Nm-1

c. When the prison is at its highest speed, the potential energy in the system is zero. So, the total energy is its maximum kinetic energy

Total energy = 1/2 mv2

= 1/2 (18)(30 X 10-3)2

= 0.0081 J

d. By conservation of energy

Total energy = K.E. + E.P.E.

0.0081 = 1/2 mv2 + 1/2 kx2

0.0081 = 1/2 (18)v2 + 1/2 (1.78)(80 X 10-3)2

Speed, v = 0.0164 ms-1

參考: Physics king

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