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:
304 meters downstream
Explanation:
The given parameters are;
The speed of the swimmer = 2.00 m/s
The width of the river = 73.0 m
The speed of the river = 8.00 m/s
Therefore;
The direction of the swimmer's resultant velocity = tan⁻¹(8/2) ≈ 75.96° downstream
The distance downstream the swimmer will reach the opposite shore = 4 × 73 = 304 m downstream
The distance downstream the swimmer will reach the opposite shore = 304 m downstream
His speed is exactly (350/27) miles per second ... about 46,667 mph. Wotta guy !
There are 120 seconds in two minutes, so to find the answer, you multiply 20 x 120 to get 2400 meters.
Answer: Hello! An objects speed is constant and has the units meters per second (m/s); thus, it does not change overtime. Acceleration is a rate of change where the speed does either increase or decrease overtime from its inital value; its units are meters per second second (m/s/s). I hope that helps!
