Answer:

Explanation:
We know that impedance of a RLC circuit is given by 
So
here R is resistance
is inductive reactance and
is capacitive reactance
To minimize the impedance
should be zero we know that 
So 


We know that 
So 

Where f is resonance frequency
Answer:
Part a)

Part b)

Explanation:
Part a)
As we know that there is no friction in the path
So here we can use energy conservation to find the distance moved by the mass
Initial spring energy = final gravitational potential energy
so we will have




Part b)
Now if spring is connected to the block then again we can use energy conservation
so we will have

so we will have



so total distance moved upwards is

Answer: k = 2π / λ
Explanation: Wavenumber k (propagation number) is a measure of spatial scale. Wavenumber can be defined as the number of wavelengths per unit distance and can be expressed in terms of lambda λ, wavelength.
This definition can be mathematically expressed as
k = 2π / λ, where k is wavenumber and λ is wavelength
<span>Jupiter is still losing the heat produced when it became a planet. Most astronomers believe that the sun, the planets, and all the other bodies in the solar system formed from a spinning cloud of gas and dust. The gravitation of the gas and dust particles packed them together into dense clouds and solid chunks of material. By about 4.6 billion years ago, the material had squeezed together to form the various bodies in the solar system. The compression of material produced heat. So much heat was produced when Jupiter formed that the planet still radiates about twice as much heat into space as it receives from sunlight. </span>