Answer to Question #103144 in Mechanics | Relativity for redoan

Question

A body of mass 25 gm is attached with a spring of spring constant 400 dynes/cm. The body is displaced by 10cm from its equilibrium position and released. Then the body executes simple harmonic motion. Calculate (i) the time period, (ii) frequency, (iii) angular frequency, (iv) maximum velocity, and (v) maximum acceleration.

Answer 1

$$k=0.4\frac{N}{m}$$

i)

$$T=2\pi\sqrt{\frac{m}{k}}=2\pi\sqrt{\frac{0.025}{0.4}}=1.57\ s$$

ii)

$$f=\frac{1}{2\pi}\sqrt{\frac{k}{m}}=\frac{1}{2\pi}\sqrt{\frac{0.4}{0.025}}=0.637\ Hz$$

iii)

$$\omega=\sqrt{\frac{k}{m}}=\sqrt{\frac{0.4}{0.025}}=4\frac{rad}{s}$$

iv)

$$v=A\omega=A\sqrt{\frac{k}{m}}=0.1\sqrt{\frac{0.4}{0.025}}=0.4\frac{m}{s}$$

v)

$$a=A\omega^2=A\frac{k}{m}=0.1\frac{0.4}{0.025}= 1.6\frac{m}{s^2}$$