A spring-mass system undergoes oscillation inside a car. If the car...

The frequency of oscillation of a spring-mass system is given by $f = \dfrac{1}{2\pi} \sqrt{\dfrac{k}{m}}$, where $k$ is the spring constant and $m$ is the mass of the block.

The frequency depends only on the mass of the block and the force constant of the spring. It is independent of the acceleration of the frame of reference.

When the car accelerates horizontally, a constant pseudo force acts on the mass. This constant force only shifts the equilibrium position of the system but does not change the restoring force constant $k$.

Since the restoring force for a displacement $x$ from the new equilibrium position remains $F = -kx$, the oscillation frequency will remain the same.