When you weigh bananas in a scale at the grocery store, the height h of the bananas is described by the differential equation d² h = dt² -kh where k is the spring constant, a constant that depends on the properties of the spring in the scale. After you put the bananas in the scale, you (cleverly) observe that the height of the bananas is given by h(t) = 4 sin 3t. What is the value of the spring constant?

When you weigh bananas in a scale at the grocery store, the height h of the bananas is described by the differential equation d² h = dt² -kh where k is the spring constant, a constant that depends on the properties of the spring in the scale. After you put the bananas in the scale, you (cleverly) observe that the height of the bananas is given by h(t) = 4 sin 3t. What is the value of the spring constant?