Question

A spring-block system undergoes simple harmonic motion on a smooth horizontal surface. The block is now given some positive charge, and a uniform horizontal electric field to the right is switched on, as a result

Answer 1

We know that SHM or the simple harmonic motion is a type of periodic motion or oscillation where the force called as the restoring force tries to displace or move the moving object to its equilibrium position.

Formula used:
$F=-kx$ , $T=2\pi\sqrt{\dfrac{m}{k}}$

Complete step-by-step solution: -
In SHM the motion of the particle which is moving in a straight line experiences an acceleration which directs the object to its equilibrium position. The common examples of SHM are the periodic oscillation of a pendulum and a system where a mass is attached to a spring which when disturbed undergoes SHM.
The elastic restoring force which puts the mass spring system in oscillation follows Hooke’s law. This can be expressed as $F=-kx$ where $F$ is the restoring force exerted by the spring with spring constant $k$ due to $x$ displacement.
The negative sign in Hooke’s law indicates that the force is restoring or opposing the motion of the system.
Consider the image given to us, clearly the given system undergoes SHM when the charged block $Q$ experiences an electric field $E$.

Then the time period $T$ of the SHM is given as
$T=2\pi\sqrt{\dfrac{m}{k}}$, where $m$ is the mass of the block and $k$ is the spring constant.
Clearly, the time period $T$ is independent of the charge or the electric field acting on the mass.

Note: In an ideal SHM, the periodic oscillation continues for an infinite amount of time if there were no dissipating energy acting on the body, like gravity and friction for example. Generally the magnitude of the acceleration depends on the displacement of the object from the equilibrium position.