Answer to Question #188471 in Mechanics | Relativity for Fadiora damilola

Question

1. Express the displacement of velocity and acceleration as a function of time

2. Express velocity and acceleration as a function of time

3. A mass of 100g is connected is a light spring of force constant 10Nm and is free to oxillate on a horizontal frictionless surface. If the mass is displaced 8cm from equilibrium and release from the rest. Find: i. The period of it's motion ii. The maximum speed of the mass iii. The maximum acceleration of the mass

Answer 1

Solution :-

Displacement $x=asin(wt+\phi)$

(a) Velocity in displace ment form

$v=\frac{dx}{dt}=aw$

Acceleration in displacement form

$a=\frac{d^2x}{dt^2}=w^2x$

(b) Acceleration in term of velocity

$a=\frac{dv }{dt}=w^2x$

(c) we know that

Kx =mg

We know that

$T=2\pi \sqrt\frac {m}{k}$

Put value

$T$ $=2\pi \sqrt\frac {m}{k}=2\pi \sqrt\frac {100\times10^{-3}}{10}=0.628sec$

T=0.628sec

Maximum speed 0.8m/sec

Maximum speed(v)=$\omega x=2\pi n(x)$

$v=\frac{2\pi}{T}x$

$v=\frac{2\pi}{0.628}\times.08=0.8m/sec$

Put values

V=0.8m/sec

Maximum acceleration

$a=\omega^2x$

Put value $a=(2\pi n)^2x$

Put value

$a=(\frac{2π}{T})^2x$

$a=(\frac{2\times3.14}{0.628})^2\times0.08$

$a=8m/sec^2$

$a=9.80m/sec^2$