Aparticle moves outward along a spiral. its trajectory is given by r = a0 where a is a constant, a = (1/r) m/rad. θ increases in time according to t2/2. where α is a constant (a) sketch the motion, and indicate the approximate velocity and acceleration at a few points (b) show that the radial acceleration is zero when θ = 1/y2 rad. (c) at what angles do the radial and tangential accelerations have equal mag nitula: ?

Industrial processes often require the damping of vibrations. consider a workbench that uses four large ideal springs in place of traditional legs, with each spring supporting one corner of the workbench and exhibiting a force constant of 47500 n/m. this workbench is used when creating products that involve highly unstable chemicals. according to specifications, the acceleration of the manufacturing equipment must be held to less than 22.3 m/s2 for the manufacturing process to proceed safely. the amplitude of vibrations are expected to remain under 0.622 mm throughout. given that the workbench and maufacturing equipment combine to 6.05 kg, find the maximum acceleration expected of the equipment and workbench. (ignore the mass of the springs.)