While on a visit to Minnesota ("Land of 10,000 Lakes"), you sign up to take an excursion around one of the larger lakes. When you go to the dock where the 1500-kg boat is tied, you find that the boat is bobbing up and down in the waves, executing simple harmonic motion with amplitude 20 cm. The boat takes 3.5 s to make one complete up-and-down cycle. When the boat is at its highest point, its deck is at the same height as the stationary dock. As you watch the boat bob up and down, you (mass 60 kg) begin to feel a bit woozy, due in part to the previous night’s dinner of lutefisk. As a result, you refuse to board the boat unless the level of the boat’s deck is within 10 cm of the dock level. Required:How much time do you have to board the boat comfortably during each cycle of up-and-down motion?

The motion of the boat is up and down in simple harmonic with amplitude of 20 cm . Time period of oscillation T = 3.5 s and top extreme point is at level with the boarding dock .

The traveller has to wait until the boat reaches middle point ( 1o cm . ) that is half its equilibrium position of oscillation .

Time period is 3.5 s . During its oscillation from extreme top position to its half of the equilibrium position , that is 10 cm below the stationary dock , time taken by boat

t = T / 12 = 3.5 /12 = .3 s .

Man shall have to wait for a period of 0.3 s

Ans 0. 3 s .