Question

For natural, undamped vibrations, the initial conditions influence which of the following?

i. Period of oscillation
ii. Natural frequency
iii. Amplitude
a) i and ii only
b) i and iii only
c) ii and iii only
d) i, ii, and iii

Answer 1

Initial conditions affect the amplitude and the initial phase, but not the period of oscillation or the natural frequency in natural, undamped vibrations.

Step-by-step explanation:

For natural, undamped vibrations, the initial conditions primarily influence the amplitude of oscillation and the initial phase. They do not affect the period of oscillation or the natural frequency of the system. The period and natural frequency are properties of the system itself, such as mass and stiffness in a spring-mass system, and the length and gravitational acceleration for a pendulum. Thus, the correct answer to the student's question is b) i and iii only, meaning that the initial conditions influence the period of oscillation (i) and amplitude (iii), but not the natural frequency (ii).