For a spring-mass oscillator, if you triple the mass but keep the stiffness the same, by what numerical factor does the period change? That is, if the original period was T and the new period is bT, what is b? It is useful to write out the expression for the period and ask yourself what would happen if you tripled the mass. b = If, instead, you triple the spring stiffness but keep the mass the same, what is the factor b? b = If, instead, you triple the mass and also triple the spring stiffness, what is the factor b? b = If, instead, you triple the amplitude (keeping the original mass and spring stiffness), what is the factor b? b =

Distance covered = speed x timethe distance traveled going against the stream = distance traveled with the stream.therefore it is the speed and the time that are the variables.as he travels the same distance both ways, speed x time is the same for each way.going upstream his speed is 4 kph; going downstream his speed is 6 kph.therefore we have two simultaneous equations: time upstream x 4 = time downstream x 6time upstream + time downstream = 60 minutestherefore we have the equation: time upstream = 6/10 hour, time downstream therefore = 4/10 hour.distance traveled at 4km/hr in 6/10 hour = 24/10 = 2.4km.check: distance traveled at 6km/hr in 4/10 hour = 24/10 = 2.4km.