Below are sets of values for the spring constant k, damping constant b, and mass m for a particle in damped harmonic motion. which of the sets takes the longest time for its mechanical energy to decrease to one-fourth of its initial value? k = k_0, b = b_0, and m = m_0 k = 3k_0, b = 2b_0, and m = m_0 k = k_0/2, b = 6b_0, and m = 2m_0 k = 4k_0, b = b_0, and m = 2 m_0 k = k_0, b = b_0, and m = 10m_0

You have been hired to design a spring-launched roller coaster thatwill carry two passengers per car. the car goes up a 10-m highhill, then descends 15m to the track's lowest point. you'vedetermined that the spring can be compressed a maximum o 2.0m andthat a loaded car will have a maximum mass of 400kg. for safetyreasons, the spring constant should be 10% larger than the minimumneeded for the car to just make it over the top. a) what spring constant (k) should you specify ? b) what is the maximum speed of a 350 kg car if the spring iscompressed the full amount.