Question

A wooden block performs SHM on a frictionless surface with frequency, v0​. The block carries a charge +Q on its surface. lf now a uniform electric field E is switched-on as shown, then what will be the SHM of the block?

Answer 1

in this question, we will understand the basic concept of a simple harmonic motion and then how the presence of external constant force affects the mean position of the wooden block. Also, we will see the simple harmonic motion of the wooden block in the presence of an electric field.

Complete answer:
As we know that a simple harmonic motion is defined as a special type of periodic motion where the restoring force on the moving object is directly proportional to the magnitude of displacement of the object and therefore it acts upon the object's equilibrium position.
Further, we know that the frequency or the time period of a simple harmonic motion depends on variable forces and it does not depend on the constant external force. Further, this constant external force can only change the mean position of the wooden block.
Here, the mean position is at the natural length of the spring in the absence of an electric field, whereas when the electric field is present the mean position of the string will be obtained after a compression.
Therefore, the simple harmonic motion or SHM of the wooden block will be of the same frequency and with shifted mean position.

Additional information:
Waves involve the transfer of energy without the transfer of the matter. So, it can be said that waves can be described as a disturbance that travels through a medium, transporting energy from one location to another location without transfer of matter.
Further, the frequency is defined as the number of waves that pass a fixed point in unit time. It can also be defined as the number of cycles or vibrations undergone during one unit of time.
Two waves are said to be coherent if they are moving with the same frequency and have constant phase difference.
The summation or adding or subtraction of all the waves travelling in a particular medium, gives us the superposition of waves. If the direction or amplitude of the waves are opposite then the superposition of waves is calculated by subtracting the waves, whereas if the two waves are travelling in the same direction or have same amplitude the resultant is given by adding up the two or more waves.
The S.I unit of frequency is Hertz or Hz and the unit of wavelength is meter or m. Furthermore we also know the S.I unit of time which is given by second or s.
Phase of a wave specifies the location of a point within a wave cycle of a repetitive waveform. Generally, the phase differences between two or more sound waves are important, rather than the actual phase of the signals. When two sound waves combine, like- the difference between the phases of the two waves is important in determining the resulting waveform.

Note:
The phase of the wave can be positive or negative depending on its direction of propagation. A sine wave starts from zero; whereas the cosine wave starts from one. In SHM we should remember that the oscillations here are sinusoidal in the small limits.