Answer:
x(t) = - 6 cos 2t
Explanation:
Force of spring = - kx
k= spring constant
x= distance traveled by compressing
But force = mass × acceleration
==> Force = m × d²x/dt²
===> md²x/dt² = -kx
==> md²x/dt² + kx=0 ------------------------(1)
Now Again, by Hook's law
Force = -kx
==> 960=-k × 400
==> -k =960 /4 =240 N/m
ignoring -ve sign k= 240 N/m
Put given data in eq (1)
We get
60d²x/dt² + 240x=0
==> d²x/dt² + 4x=0
General solution for this differential eq is;
x(t) = A cos 2t + B sin 2t ------------------------(2)
Now initially
position of mass spring
at time = 0 sec
x (0) = 0 m
initial velocity v= = dx/dt= 6m/s
from (2) we have;
dx/dt= -2Asin 2t +2B cost 2t = v(t) --- (3)
put t =0 and dx/dt = v(0) = -6 we get;
-2A sin 2(0)+2Bcos(0) =-6
==> 2B = -6
B= -3
Putting B = 3 in eq (2) and ignoring first term (because it is not possible to find value of A with given initial conditions) - we get
x(t) = - 6 cos 2t
==>
Answer:
80 amperes
Explanation:
Current in the circuit = ?
Voltage in the circuit = 160 Volts
Resistance = 2 Ω
Voltage = Current x Resistance
V = IR
160V = I x 2 Ω
I = 160V / 2 Ω
I = 80 Amperes
Therefore the current in the circuit is 80 amperes :)
Replication, Multiplication, and Substitution.
<h2>
The magnitude of the force that acts on a charge of -7.9C at this spot is 2.21 x 10⁶ N.</h2>
Explanation:
Electric field is the ratio of force and charge.
Electric field, E = 280000 N/C
Charge, q = -7.9 C
We have
The magnitude of the force that acts on a charge of -7.9C at this spot is 2.21 x 10⁶ N.
