Final answer:
The frequency of a simple harmonic motion can be calculated by the formula, where the frequency is inversely proportional to the period and depends on the mass of the system and the stiffness equivalent of the 'spring'.
Step-by-step explanation:
The frequency of an object in simple harmonic motion (SHM) can be determined by understanding the qualities of SHM, as demonstrated in systems like a mass attached to a spring. For such a system, Hooke's law describes the restoring force which is directly proportional to the displacement and is always directed towards the equilibrium position.
In SHM, the frequency (ƒ) of oscillation is inversely proportional to the period (T) and can be calculated using the formula ƒ = 1/T. When a marble oscillates inside a hemispherical bowl, the force you apply to maintain this motion is similar to the restoring force acting on a mass-spring system, allowing it to oscillate with a frequency characteristic of its mass and the stiffness of the equivalent 'spring' or the shape of the bowl.
The formula for frequency of a simple harmonic oscillator is dependent on the stiffness of the spring (k) and the mass (m) in the system, given by ƒ = (1/2π) * √k/m. The actual frequency of the marble in the bowl would also be dependent on the effective 'spring constant' and mass of the marble, which would in reality be a bit more complex due to the shape of the bowl not being a perfect hemisphere and the friction present in the system.