Modelling the volume of a container/differentiation.

Question 1 A bucket-shaped container has a circular base of radius 10 cm, and its slant height is 30 cm. the radius of the open circular top of the container is 10x cm. the curved surface of the container is modeled by part of a cone, as shown below. Please see attached.

Damping and resonance problem

Hi, I think I have managed to do parts (a) and (b) successfully (but could do with a confidence check!) but had a problem with part (c): I cannot figure out where the my: comes from on the RHS of the equation. I am taking the x origin from the top of the device and pointing downwards, which I am unsure is correct since the y origin points upwards. I can reach the equation by, when using Newton's Second Law (F=ma), I take the acceleration to be the sum of x: and y:, thus expanding to give the correct answer. But I have a feeling I am just making this up and will not gain full marks for the question ...

Direction and Magnitudes of Support Reactions; Load and Nature of Load of Canopy

I need a worked solution for these questions (also attached on the LAST PAGE of the attachement. The first couple pages are just examples. Thanks) Given the attached info, please determine: a) the direction sof the support reactions by locating the point ... b) the magnitudes of the reactions and the load in each member of the canopy ... c) the nature of the load in each of the canopy mambers ... Thanks! (Please see attached for complete questions)

Damping and resonance problem

Please help with this damping and resonance problem...I have been working on it for several days but to no avail. Thank you

Modelling and Simulation

Please see the attached file the Modelling and Simulation