"within the specified time" is a correct and usable phrase in written English.
You can use it when referring to an amount of time that has been previously mentioned and established. For example, "Please finish the project within the specified time of two weeks."
Eircom says it has had difficulty providing enough capacity within the specified time frame.
Disagreement emerged about which decisions fell within the specified time frame.
The act had to occur within the specified time period (1960-1994).
The I.N.S. did not serve notices of the immigration charges on these detainees within the specified time frames.
A student who fails to take corrective steps within the specified time limit will be terminated from candidacy for his/her degree.
An employee who does not provide the required evidence or medical certification within the specified time period is not entitled to sick leave.
The wide lateral surface area of the heat spreader represented that the area adversely influenced the amount of molten urea-water solution within the specified time period.
An 'Incomplete' grade can be made up in a manner specified by the department or teaching group within a reasonable time; if the deficiency is not made up within the specified time, the 'Incomplete' grade becomes a 'Fail' grade.
As McMenamy thereafter, with Dietrich's knowledge, spent time and money in doing work under the contract, Dietrich is equitably estopped from setting up the failure to complete within the specified time as a defense to the present suit.
If Mirelis fails to close any and all U.S.-related accounts classified as "dormant" within the specified time period, it must provide periodic reporting at the request of the Tax Division.
If NPB fails to close any and all U.S.-related accounts classified as "dormant" within the specified time period, it must provide periodic reporting at the request of the Tax Division.
