Answer:
Explanation:
The spring mass equation for the damped oscillation will be,
Here, -bv is the damping term used in this b is damping constant, k is spring constant, x is elongation in the spring, F is the force.
Therefore the differential equation for the damped harmonic oscillator is,
Answer:
D . 1.47 x 10⁻² Ω-m
Explanation:
L = length of the cylindrical resistor = 2 m
d = diameter = 0.1 m
A = Area of cross-section of the resistor = (0.25) d² = (0.25) (3.14) (0.1)² = 0.785 x 10⁻² m²
V = battery Voltage = 12 volts
= current flowing through the resistor = 3.2 A
R = resistance of the resistor
Resistance of the resistor is given as
R = 3.75 Ω
= resistivity
Resistance is also given as
= 1.47 x 10⁻² Ω-m
Explanation:
The frequency is given to be f = 8 Hz.
Period is the inverse of frequency.
T = 1/f = 0.125 s
Velocity is wavelength times frequency.
v = λf = (0.40 m) (8 Hz) = 3.2 m/s
The wave travels 3.2 meters every second.
Answer:
d = 3.44 x 10⁸ m
Explanation:
The minimum distance required will be the distance from the centre of the earth to a point where gravitational intensity due to both earth and moon becomes equal . Once this point is reached , moon will attract the baseball on its own .
Let this distance be d from the centre of the earth
So GM / d² = G m / ( 3.82 x 10⁸ - d )²
M is mass of the earth , m is mass of the moon
M / m = ( d / 3.82 x 10⁸ - d )²
5.972 x 10²⁴ / 7.34 x 10²² = ( d / 3.82 x 10⁸ - d )²
81.36 = ( d / 3.82 x 10⁸ - d )²
9.02 = d / 3.82 x 10⁸ - d
34.45 x 10⁸ - 9.02 d = d
34.45 x 10⁸ = 10.02 d
d = 3.44 x 10⁸ m