Answer:
a) t=24s
b) number of oscillations= 11
Explanation:
In case of a damped simple harmonic oscillator the equation of motion is
m(d²x/dt²)+b(dx/dt)+kx=0
Therefore on solving the above differential equation we get,
x(t)=A₀
where A(t)=A₀
A₀ is the amplitude at t=0 and
is the angular frequency of damped SHM, which is given by,

Now coming to the problem,
Given: m=1.2 kg
k=9.8 N/m
b=210 g/s= 0.21 kg/s
A₀=13 cm
a) A(t)=A₀/8
⇒A₀
=A₀/8
⇒
applying logarithm on both sides
⇒
⇒
substituting the values

b) 

, where
is time period of damped SHM
⇒
let
be number of oscillations made
then, 
⇒
Answer:
the money that would be saved is $13.14.
Explanation:
Given;
power consumed by the light bulb, P = 100 W = 0.1 kW
time of running the bulb, t = 3 hours for 365 days = 1,095 hours
cost rate of power consumption, C = $0.12 per kWh
Energy consumed by the light bulb for the given days;
E = Pt
E = 0.1 kW x 1,095 hr
E = 109.5 kWh
Cost of energy consumed = 109.5 kWh x $0.12 / kWh
= $13.14
Therefore, the money that would be saved is $13.14.
The answer is Monocline. And I checked it, it's correct.
Answer:
The velocity is 40 ft/sec.
Explanation:
Given that,
Force = 3200 lb
Angle = 30°
Speed = 64 ft/s
The resistive force with magnitude proportional to the square of the speed,

Where, k = 1 lb s²/ft²
We need to calculate the velocity
Using balance equation

Put the value into the formula

Put the value of k


At terminal velocity 
So, 


Hence, The velocity is 40 ft/sec.
Decrease the amount of force applied