A research probe lands on a newly discovered planet. The pro…
A research probe lands on a newly discovered planet. The probe contains:a spring-mass system used to measure oscillations,a gas thermometer,and a motion sensor that tracks vertical motion.The probe drops a small mass from rest from a height of h, measures the local gravitational acceleration g, and then uses the same mass attached to a spring to study oscillatory motion. During the experiment, the temperature of the environment increases significantly.Answer the following:(a)Using calculus-based kinematics, derive an expression for the speed of the falling object just before it hits the ground if air resistance is negligible.(b)The mass is attached to a spring of spring constant k. Derive the angular frequency and period of oscillation of the system.(c)Suppose the temperature increase causes the spring constant to decrease slightly because the material softens. Explain qualitatively and mathematically how this affects the period of oscillation.