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 smallest effort = 300N
Explanation:
Using one of the condition for the attainment of equilibrium:
Clockwise moment = anticlockwise moments
900 × 1 = 3 × M
Where M = the weight of the strong man
3M = 900
M = 900/3 = 300N
Therefore, 300N is the smallest effort that the strongman can use to lift the goat
Answer:
Friction can be increased the longer two objects are rubbed together, since the longer they are rubbed is the more heat produced.
Explanation:
Answer:
7.92 m/s
Explanation:
= Mass of raindrop = 
= Mass of mosquito
= Initial Velocity of raindrop = 8.1 m/s
= Initial Velocity of mosquito = 0 m/s
= Velocity of center of mass
For elastic collision

Hence, the velocity of the attached mosquito, falling immediately afterward is 7.92 m/s
Answer: 1872 N
Explanation:
This problem can be solved by using one of the Kinematics equations and Newton's second law of motion:
(1)
(2)
Where:
is the bullet's final speed (when it leaves the muzzle)
is the bullet's initial speed (at rest)
is the bullet's acceleration
is the distance traveled by the bullet before leaving the muzzle
is the force
is the mass of the bullet
Knowing this, let's begin by isolating
from (1):
(3)
(4)
(5)
Substituting (5) in (2):
(6)
Finally:
