Answer:
distance between the dime and the mirror, u = 0.30 m
Given:
Radius of curvature, r = 0.40 m
magnification, m = - 2 (since,inverted image)
Solution:
Focal length is half the radius of curvature, f = 
f = 
Now,
m = - 
- 2 = -
= 2 (2)
Now, by lens maker formula:


v =
(3)
From eqn (2):
v = 2u
put v = 2u in eqn (3):
2u = 
2 = 
2(u - 0.20) = 0.20
u = 0.30 m
Answer:
False
Explanation:
When the location of the poles changes in the z-plane, the natural or resonant frequency (ω₀) changes which in turn changes the damped frequency (ωd) of the system.
As the poles of a 2nd-order discrete-time system moves away from the origin then natural frequency (ω₀) increases, which in turn increases damped oscillation frequency (ωd) of the system.
ωd = ω₀√(1 - ζ)
Where ζ is called damping ratio.
For small value of ζ
ωd ≈ ω₀
Explanation:
Given that,
Size of object, h = 0.066 m
Object distance from the lens, u = 0.210 m (negative)
Focal length of the converging lens, f = 0.14 m
If v is the image distance from the lens, we can find it using lens formula as follows :
(a) Magnification,

(b) Magnification, 
h' is image height

Hence, this is the required solution.
Answer:
configuration of string:
Node - Antinode - Node or N-A-N
This is 1/2 wavelength since a full wavelength is N-A-N-A-N
f (fundamental) = V / wavelength
F0 = 300 m/s / 1 m = 100 / sec
F1 = 300 m/s / .5 m = 600 / sec
Each increase is a multiple of the fundamental since the wavelength
increases by 1/2 wavelength to keep nodes at both ends of the string