The position of a vibrating spring after t seconds is given by f(t) = (1/2) cost − (1/5) sin t meters. Positive and negative values of f(t) mean that the spring is to the right and the left of its equilibrium position, respectively. Find the position, the velocity, and acceleration of the spring at t = 1.
The position of a vibrating spring after t seconds is given by f(t) = (1/2) cost − (1/5) sin t meters. Positive and negative values of f(t) mean that the spring is to the right and the left of its equilibrium position, respectively. Find the position, the velocity, and acceleration of the spring at t = 1.
The given position of a vibrating spring is , where t is the time in seconds.
Evaluate the position of the spring at t=1 as follows.
Therefore, the position of the spring at t=1 is 0.102 m to the right of the equilibrium position.
Evaluate the velocity of the spring as follows.
Evaluate the velocity at t=1 as follows.
Therefore, the velocity of the spring at t=1 is -0.523 m/sec.
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