Methods and apparatus to control movement of a component are disclosed herein. An example apparatus includes a housing defining a bore and a piston disposed inside the bore. The piston is to be coupled to a movable component disposed outside of the bore. The example apparatus further includes a fluid flowline in fluid communication with a first chamber of the bore and a second chamber of the bore. The first chamber is on a first side of the piston, and the second chamber on a second side of the piston. The example apparatus also includes a valve to control fluid flow through the fluid flowline. The valve is to be in a first state to enable the piston to dampen movement of the component, and the valve is to be in a second state to enable the piston to hold the component substantially stationary.