Final answer:
Doubling the amplitude of an oscillating weight in a spring-mass system in simple harmonic motion has no effect on the period or phase shift of the system.
Step-by-step explanation:
When the amplitude of a spring-mass system oscillating in simple harmonic motion (SHM) is doubled, the period of the oscillation remains unchanged. The period of a simple harmonic oscillator is dependent on the mass of the object and the spring constant of the spring and is given by the formula T = 2π√(m/k), where T is the period, m is the mass of the object, and k is the spring constant. Since the amplitude does not appear in this equation, altering the amplitude does not affect the period of an SHM system. Similarly, the phase shift of the oscillation is not affected by a change in amplitude, as it is determined by the initial conditions of the motion, such as the initial displacement and velocity.