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:
the Princess in "St. George and the Dragon"
Answer:
x component is 60.60 N and y component is 35 N ⇒ answer A
Explanation:
A boy is pulling a wagon with a force of 70.0 N directed at an angle
of 30 degrees above the horizontal then,
is the horizontal component of the force in the direction
of positive part of x-axis
is the vertical component of the force force in the direction
of positive part of y-axis
The x component of the force is the force multiplied by
cos(30)°
The y component of the force is the force multiplied by
sin(30)°
→ The x component = F cos(30)
→ The x component = 70 cos(30) = 60.60 N
→ The y component = F sin(30)
→ The y component = 70 sin(3) = 35 N
<em>x component is 60.60 N and y component is 35 N</em>
The property that metalloids share with nonmetals are
Both can react to form acidic compounds
