Question

A spring-loaded pendulum with a mass of 500 g, elastic coefficient of 0.5 N / cm oscillates in the lips

The field has a drag coefficient of 0.5 kg / s.

a. Determine the period and reduce the logarithm of the system.

b. After how long does the energy decrease 90%.

c.People exert a forced force

F= 2cos20πt N

into the system then the equation

oscillation of the generation like?

d. With any frequency of forced external force, the amplitude reaches its maximum value and value equals 4N

Answer 1

a)

$$T=2\pi\sqrt{\frac{1}{\frac{50}{0.5}-\frac{0.5^2}{4(0.5)^2}}}=0.63\ s$$

$$\gamma=\frac{0.5}{2(0.5)}=0.5\ Hz$$

b)

$$0.9=e^{-0.5t}\\t=0.21\ s$$

c)

$$0.5a+0.5v+50x=2\cos{20πt}$$