Answer:
x(t)=0.337sin((5.929t)
Explanation:
A frictionless spring with a 3-kg mass can be held stretched 1.6 meters beyond its natural length by a force of 90 newtons. If the spring begins at its equilibrium position, but a push gives it an initial velocity of 2 m/sec, find the position of the mass after t seconds.
Solution. Let x(t) denote the position of the mass at time t. Then x satisfies the differential equation
Definition of parameters
m=mass 3kg
k=force constant
e=extension ,m
ω =angular frequency
k=90/1.6=56.25N/m
ω^2=k/m= 56.25/1.6
ω^2=35.15625
ω=5.929
General solution will be
differentiating x(t)
dx(t)=-5.929c1sin(5.929t)+5.929c2cos(5.929t)
when x(0)=0, gives c1=0
dx(t0)=2m/s gives c2=0.337
Therefore, the position of the mass after t seconds is
x(t)=0.337sin((5.929t)
Compute the ball's angular speed <em>v</em> :
<em>v</em> = (1 rev) / (2.3 s) • (2<em>π</em> • 180 cm/rev) • (1/100 m/cm) ≈ 4.917 m/s
Use this to find the magnitude of the radial acceleration <em>a</em> :
<em>a</em> = <em>v </em>²/<em>R</em>
where <em>R</em> is the radius of the circular path. We get
<em>a</em> = <em>v</em> ² / (180 cm) = <em>v</em> ² / (1.8 m) ≈ 13.43 m/s²
The only force acting on the ball in the plane parallel to the circular path is the tension force. By Newton's second law, the net force acting on the ball has magnitude
∑ <em>F</em> = <em>m</em> <em>a</em>
where <em>m</em> is the mass of the ball. So, if <em>t</em> denotes the magnitude of the tension force, then
<em>t</em> = (1.6 kg) (13.43 m/s²) ≈ 21 N
By using the Ohms law, we can calculate the current.
Ohms law,

Here, V is potential difference, and R is the resistance.
Given,
and
.
Therefore, putting the given values in above relation , we get

or
Thus, the current is drawn by a television 4 Ampere
Answer:
I hypothesis that the motion involving the balls in the experiment were moving to create data.
Explanation:
I hope this helps!