Answer:
Explanation:
Given that:
the initial angular velocity 
angular acceleration 
= 4.44 rad/s²
Using the formula:
Making t the subject of the formula:
where;
∴
t = 0.345 s
b)
Using the formula:
here;
= angular displacement
∴
Recall that:
2π rad = 1 revolution
Then;
0.264 rad = (x) revolution
x = 0.042 revolutions
c)
Here; force = 270 N
radius = 1.20 m
The torque = F * r
However;
From the moment of inertia;
given that;
I = 84.4 kg.m²
For re-tardation; 
Using the equation
t = 0.398s
The required time it takes= 0.398s
Divide distance by the time it takes to travel that distance
the formula for time is divide distance/speed
Answer:
x(t) = d*cos ( wt )
w = √(k/m)
Explanation:
Given:-
- The mass of block = m
- The spring constant = k
- The initial displacement = xi = d
Find:-
- The expression for displacement (x) as function of time (t).
Solution:-
- Consider the block as system which is initially displaced with amount (x = d) to left and then released from rest over a frictionless surface and undergoes SHM. There is only one force acting on the block i.e restoring force of the spring F = -kx in opposite direction to the motion.
- We apply the Newton's equation of motion in horizontal direction.
F = ma
-kx = ma
-kx = mx''
mx'' + kx = 0
- Solve the Auxiliary equation for the ODE above:
ms^2 + k = 0
s^2 + (k/m) = 0
s = +/- √(k/m) i = +/- w i
- The complementary solution for complex roots is:
x(t) = [ A*cos ( wt ) + B*sin ( wt ) ]
- The given initial conditions are:
x(0) = d
d = [ A*cos ( 0 ) + B*sin ( 0 ) ]
d = A
x'(0) = 0
x'(t) = -Aw*sin (wt) + Bw*cos(wt)
0 = -Aw*sin (0) + Bw*cos(0)
B = 0
- The required displacement-time relationship for SHM:
x(t) = d*cos ( wt )
w = √(k/m)
