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Robots with telescoping arms are sometimes used to perform tasks (e. g., welding or placing screws) where access may be difficult for other robotic types. during a test run, a robot arm is programmed to extend according to the relationship r = 3 + 0.5cos(4θ) and the arm rotates according to the relationship θ=−π4t2+πt , where r is in feet, θ is in radians, and t is in seconds. use a computer program to plot the path of tip a in x and y coordinates for 0 ≤ t ≤ 4s.

Asequential circuit contains a register of four flip-flops. initially a binary number n (0000 ≤ n ≤ 1100) is stored in the flip-flops. after a single clock pulse is applied to the circuit, the register should contain n + 0011. in other words, the function of the sequential circuit is to add 3 to the contents of a 4-bit register. design and implement this circuit using j-k flip-flops.

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