A weight attached to the end of a long spring hanging above the ground is bouncing...

 

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A weight attached to the end of a long spring hanging above the ground is bouncing up and down. As it bounces, its distance from the floor varies sinusoidally with time (assume no friction is present in the spring). A stopwatch is used to measure its height above the floor as a function of time. When the stopwatch reads 0.3 s, the weight first reaches a high point 60 m above the floor. The next low point, at 40 cm above the floor, occurs at 1.8 s. (a) Draw a sketch to illustrate d, the spring's distance from the floor in centimeters, over the interval 0 ≤t≤ 6 where t is in seconds. (b) Determine a function, d(t), that describes the spring's distance from the floor as a function of time. (c) What is the distance from the floor (to the nearest millimeter) when the stopwatch reads 8.1 s? (d) At what time is the weight 45 cm above the floor for the first time? A weight attached to the end of a long spring hanging above the ground is bouncing up and down. As it bounces, its distance from the floor varies sinusoidally with time (assume no friction is present in the spring). A stopwatch is used to measure its height above the floor as a function of time. When the stopwatch reads 0.3 s, the weight first reaches a high point 60 m above the floor. The next low point, at 40 cm above the floor, occurs at 1.8 s. (a) Draw a sketch to illustrate d, the spring's distance from the floor in centimeters, over the interval 0 ≤t≤ 6 where t is in seconds. (b) Determine a function, d(t), that describes the spring's distance from the floor as a function of time. (c) What is the distance from the floor (to the nearest millimeter) when the stopwatch reads 8.1 s? (d) At what time is the weight 45 cm above the floor for the first time?