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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)
Answer:
Explanation:The rotational inertia of any object depends directly on the distance the mass is from the axis of a rotating object
Having more mass at the sides will increase the rotational inertia of the object that is why a Hollow sphere having same M and R as the solid one has more rotational inertia as it has more mass at the sides.
The sphere have some mass at the center but most of its mass is closer to its radius and thus have more inertia than flat Disk.
The same relation exist between a flat disk and hollow sphere. The hollow sphere have some mass at the center but most of its mass is closer to its radius and thus have more inertia.
The rotational of the objects can be calculated by these equations
Answer:
chemical energy is converted to electrical energy in a voltaic cell.
Sam’s weight is 88.1 pounds
